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PROCEEDINGS
Cambridge Philosophical Society.
VOLUME IX.
Cambridge :
PRINTED BY J. AND C. F. CLAY,
AT THE UNIVERSITY PRESS.
PROCHEDINGS
OF THE
CAMBRIDGE PHILOSOPHICAL
SOCIETY.
VOLUME IX.
OcTOBER 28, 1895—May 16, 1898.
Cambridae :
PRINTED AT THE UNIVERSITY PRESS,
AND SOLD BY
DEIGHTON, BELL AND CO. AND MACMILLAN AND CO. CAMBRIDGE.
BELL AND SONS, LONDON.
1898
CONTENTS.
VOL. IX.
October 28, 1895.
Annual General Meeting
November 11, 1895.
A method of measuring the loss of energy in Hysteresis. By G. F. C,
Searle 3 , - :
On the forms of cubic ee confainine 27 mal ay na fee (Plates
I—Il). By W. H. Blythe ‘
Expansion produced by Electric Discharge. By Miss Tee
November 25, 1895.
Exhibition of a curious specimen of Travertine lining a wooden pipe:
By Prof. T. McK. Hughes
On Symmetry in the foliage of a Beauek of Mulberr 4 ath Pavdniietce
in the individual leaves. By Prof. T. McK. Hughes
The Origin of Vertebrates. By Dr W. H. Gaskell
December 2, 1895.
Discussion on Dr Gaskell’s Paper . < : .
January 27, 1896.
Longitudinal Electric Waves, and Réntgen’s X Rays. By Prof. J. J.
Thomson
The Equilibrium of feptropic ‘Blastic Solid Shells of nearly Spherical
form. By Dr C. Chree
Distribution of Solar Radiation, and i dégendencs on Wecionoriienl
Elements. By R. Hargreaves
PAGE
37
61
69
vi Contents.
February 10, 1896.
On an Osmometer. By Dr Lazarus Barlow . ° : :
On the communication between peritoneal cavity And Sa veins
through the nephrostomial tubules in the frog. By E. J. Bles
On the effect of water currents on the assimilation of ae plants.
By F. Darwin and Miss D. F. M. Pertz . : ‘
On a collection of plants from New Britain (Neu poner yy By lee
Burkill
February 24, 1896.
Experiments on Liquid Air. By Prof. Dewar :
On the Generalization of certain Properties of the Tisheiheiban. By
J. Brill
On the absolute Me neern i Optical Deretien "bap a Soren By a
Larmor . : : : : . : : - :
March 9, 1896.
Notes on the Geological History of Monocotyledons. By A. C. Seward
A description of the Crania found at Girton in 1881. By R. J. Horton-
Smith : :
On the Recurrence of ie Nese By Bron Ake McK. Hheties :
On some Chipped Flints from the Plateau Gravel of Salisbury and
elsewhere. By Prof. T. McK. Hughes
On the Leakage of Electricity through Dielectrics sexowed by Rontgen
Rays. By Prof. J. J. Thomson and J. A. M°Clelland
April 27, 1896.
On photographing the whole length of a Spectrum at once. By Prof.
Liveing : F , :
On dioxymaleic fea and fg edness By H. J. H. Fenton
On the atomic weight of Oxygen. By A. Scott :
On the combining volumes of Carbon Monoxide and Onan. By
A. Scott : :
The constituents of Tada hems resin. ey T. Jel, Hasterfield ol TB;
Wood : : :
Note on the Brirmeclonieall mecien of canines resin. By C. BR.
Marshall .
May 11, 1896.
Note on the formation of the germinal layers in aug By
EK. W. Mac Bride
Note on the continuity of Mesenchynne one in “EEE tei ve. By
E. W. Mac Bride
Crania from Teneriffe. By F. C. Sherpa
PAGE
111
114
120
126
141
142
143
144
144
149
150
153
154
Contents.
May 25, 1896.
On the spectroscope used in connexion with the 25-inch refractor. By
H. F. Newall F : : : i
On a suggestion for a form of SpoderolicliogneBh: By H. F. Newall
On the Period of the Earth’s Free Eulerian Precession. By J. Larmor.
Note on a point in theoretical dynamics. By Sir Robert Ball
On the maximum deviation of a ray of light by a prism. By Prof.
A. Anderson : : : .
On a method of discussing the plane satus of satiabons “By A.C.
Dixon
October 26, 1896.
Annual General Meeting ; : ; 4
On the casts of Zyuanodon bernissartensis, Pouloneee By 8S. F. Harmer
On the proposed relationship of Birds and Dinosaurs. By H. Gadow
On Cyclostomatous Polyzoa. By 8. F. Harmer
November 9, 1896.
On the Nature of the Réntgen Rays. By Prof. Sir G. G. Stokes
On certain cases of Discharge in Vacuo and on the zigzag path of
Lightning. By J. Monckman .
November 23, 1896.
On the Superficial Colour of a Silver-Zine Alloy. ne Cor ane
and F. H. Neville
On Thermometric “ Fixed Points.” “Re E. H. Griffiths - :
January 25, 1897.
On some results obtained by staining the Brain with the Chrome-silver
method (télustrated by photo-micrographs). By Dr Hill .
On a possible explanation of the quinqueloculine arrangement of the
chambers in the young of the microspheric forms of Triloculina
and Biloculina. By J. J. Lister : :
On the theory of Osmotic Pressure. By J. Larmor
February 8, 1897.
On the Cathode Rays. By Prof. J. J. Thomson
On Electricity in Gases and the formation of Clouds in Hinged eases
By J. 8. Townsend
Vili
PAGE
179
179
183
193
222
224
Vill Contents.
February 22, 1897.
On the Diffraction Pattern near the Focus of a ae By
R. H. D. Mayall
On the marks made by stars on Theta mates eepowel near he
focus of a telescope. By H. F. Newall :
On Theorems on the contacts of spheres. By W. M°F. Om ,
On change of the independent variable in a coefficient. By E. G. Gallop
March 8, 1897.
On the injection of the intercellular spaces occurring in the leaves of
Elodea during recovery from plasmolysis. By F. Darwin and
Miss Pertz
On the phenomena of (arbor [Droste reduction associated! wee
reduced vitality in plants. By F. F. Blackman .
On the leaves of Bennettites. By A. C. Seward
April 26, 1897.
On Lie’s Solution of a Partial Differential Equation of the First Order.
By Dr Dixon
On the Apparent Bileceiaeation in an istlestinte Field a ie Bounding
Surface of Two Dielectrics. By A. Anderson .
On Luminosity attending the compression of certain mameedt gases. By
H. F. Newall
May 10, 1897.
Observations on Stomata by a new method. By F. Darwin
Notes on hybrid Cinerarias produced a Mr Lynch and Miss Porte
By W. Bateson : ; : ; : :
May 24, 1897.
The relationship of Amphiowus and Balanoglossus. By EK. W. MacBride
On the degree of the Eliminant of Two Algebraic Equations. By Dr
Lachlan 4 : F :
Tides on the veces mieory: “Oe Dr Chree .
Experiments on the Effect of Ultra-violet Light on the @onducheres of
Iodine Vapour. By J. Henry. : 5 : :
October 25, 1897.
Annual General Meeting : : : : :
Electrical Oscillations in Wires. By H. C. Pocklington
On Circles, Spheres and Linear Complexes. By J. H. Grace
Reduction of a certain Multiple Integral. By Arthur Black .
On the Gamma Function. By H. F. Baker :
On the lines of striction of a hyperboloid. By H. F. Baker
On the Action of Uranium rays on the Condensation of Water Vapene
By C. T. BR. Wilson .
PAGE
259
269
271
272
272
273
273
279
292
295
303
308
309
313
318
319
323
324
332
332
302
333
333
Contents.
November 8, 1897.
Farmer’s method of demonstrating assimilation. By Francis Darwin .
Artificial Cultures of Sterewm, a Tae eg Fungus. By Prof.
Marshall Ward : : ;
On Encephalartos Ghellinckir, iene a rare Cet By A. C. Seward
November 22, 1897.
Partial Differential Equations of the Second Order. By Prof. Forsyth .
Electrical Properties of Newly Prepared Gases. By John 8. Townsend
A chemical effect produced by the impact of kathode rays. By Prof.
J. J. Thomson and 8. Skinner . : : :
The effect of zinc and other metals on a Aire one pine By Prof.
J.J. Thomson .
December 6, 1897.
Notes on some Hawaiian Insects. By R. C. L. Perkins
Remarks on a journey to investigate the habits and dev ‘leprae of
Lepidosiren paradoxa. By J. Graham Kerr
January 24, 1898.
A New Method in Combinatory Analysis with applications to Latin
Squares and associated questions. By Major P. A. MacMahon
Abelian Functions in connexion with two-dimensional fluid motions.
By H. F. Baker
On the production of a cloud by the action of lee violet fight on anv
air. By C. T. R. Wilson
On the use of logarithmic coordinates in Physics ne J a ie paneate
On the Diffuse Reflection of Réntgen Rays. By Prof. J. J. Thomson
February 7, 1898.
Some Zoological Results of a Voyage to Melanesia during the years
1894—1897. By Arthur Willey
February 21, 1898.
On some differential equations in the theory of gies algebra. By
Prof. Forsyth : : : :
The Discharge of Electrification by Ultra- moles iaene By E. Ruther-
ford . : : :
Rontgen photoerape of. ertallic alow ey C. T. ercoce and F. H.
Neville : : ‘ : : apouis : ‘ :
1x
PAGE
338
340
340
345
345
371
372
373
380
381
381
392
393
363
398
x Contents.
March 7, 1898.
The Coral Reefs of Funafuti, Rotuma and Fiji together with some
Notes on the Structure and Formation of Coral Reefs in general.
By J. Stanley Gardiner
Method for the Demonstration of “ Gonnecting Threads Zain ae Cell
Wall. By Walter Gardiner
May 2, 1898.
On the theory of Order. By E. T. Dixon :
On a certain system of differential equations donate pociedie fon cHone
By H. F. Baker : : 5 ,
On the Total Eclipse of the oun 1898 fon 22, By H. F. Newall .
May 16, 1898.
On the figures produced on photographic plates by electric —
By J. A. M°Clelland
On a Method of facilitating the Tacasiverent of tempentine by means
of Platinum Thermometry. By EK. B. H. Wade
The development of Peripatus novae-britanniae. By Dr A. Willey
On the possibility of deducing magneto-optic phenomena from a direct
modification of an electro-dynamic energy function. By J. G.
Leathem .
On the solutions of the aruenion (Cue O in elliptic coordinates
and their physical applications. By R. C. Maclaurin
On the interpretation of divergent solutions of the hyper- ocomenee
equation. By W. MCF. Orr
The Harmonic Expression of the Daily Variation of Solar Radiation,
and the Annual Variation of its coefficients. By R. Hargreaves
INDEX
PLATES.
Tand II. To illustrate Mr Blythe’s paper .
III. To illustrate Mr J. Stanley Gardiner’s paper
IV and V. To illustrate Mr M®Clelland’s paper
PAGE
417
551
531
532
PROCEEDINGS
OF THE
Cambridge Philosophical Society.
ANNUAL GENERAL MEETING.
Monday, 28 October 1895.
PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR.
The following officers and new members of Council were
elected :-—
President :
Prof. J. J. Thomson.
Vice-Presidents :
Prof. T. McKenny Hughes, Mr F. Darwin, Prof. G. D. Liveing.
Treasurer:
Mr Glazebrook.
Secretaries :
Mr Larmor, Mr Newall, Mr Bateson.
New Members of Council:
Prof. Sir G. G. Stokes, Mr A. Sedgwick, Mr A. Scott.
The names of the Benefactors were read.
The President referred to the death of Prof. Babington and
of Prof. Huxley.
VOL, IX, PT. I. 1
2 Mr Searle, A method of measuring the [Noy. 11,
The following resolutions were proposed by Prof. Liveing,
seconded by Prof. Hughes, and carried unanimously.
“That this meeting desires to place on record its sense of the
loss the Society has sustained by the death of Prof. Babington
and to convey to Mrs Babington the expression of their sympathy
and condolence in her bereavement.”
“That the President be requested to convey to Mrs Babington
the foregoing resolution.”
The following resolutions were proposed by Prof. Newton,
seconded by Prof. G. H. Darwin, and carried unanimously.
“That the Fellows of the Cambridge Philosophical Society at this
their first meeting since the death of the Rt. Hon. Thomas Henry
Huxley, LL.D., desire to express their sympathy with Mrs Huxley,
and to record their sense of the depth of his influence on modern
thought and on the progress of Biological Science.”
“That the President be requested to convey to Mrs Huxley the
foregoing resolution.”
Monday, 11 November 1895.
PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR.
The following Communications were made to the Society :
(1) A method of measuring the loss of energy in Hysteresis.
By G. F. C. Seare, M.A., Peterhouse.
The extensive employment of transformers in the distribution
of energy by alternating electric currents has caused the measure-
ment of hysteresis in iron to become a matter of such commercial
importance as to stimulate efforts to find a means for readily
testing iron as to its quality with respect to hysteresis. The
subject is important not only commercially but also from the
purely scientific point of view, for it can hardly be doubted that
our knowledge of the molecular structure of iron would receive
some extension if a means were provided by which the effects of
various physical conditions—stress, temperature, the passage of
electric currents &c.—upon the loss of energy in hysteresis could
be investigated with a comparatively small expenditure of time.
As is well known, the loss of energy occasioned by any cyclic
change in the magnetization of iron is equal to f[HdJ in ergs
per cubic cm. of iron per complete cycle, H denoting the magnetic
force and J the intensity of magnetization, both im ©.G.s. units.
The waste of energy, fHdJ, I shall denote by W. The value of
fHdI may be obtained by plotting in a curve the simultaneous
values of H and J from a numerous series of observations, and
1895.] loss of energy in Hysteresis. 3
then measuring the area of the curve. Or again, since, if B is the
magnetic induction, we have B= H + 47TJ so that
(for [HdH vanishes when applied to a cyclic change), it follows
that the hysteresis loss may be determined by plotting and
measuring the curve given by simultaneous values of B and H.
To obtain any satisfactory curve at least a dozen simultaneous
observations of H and B are needed.
I have striven to design a method which should enable the
hysteresis loss to be determined by a single observation of the
“throw” of a spot of light along a scale. The method was far
from being perfected when this communication was made to the
Society on 11 Noy. 1895, but it has been represented to me that
though at present imperfect it is of sufficient interest and promise
to justify its finding a place in the Society’s pages.
A bar of iron of cross section A is placed in a solenoid wound
with WV turns of wire per cm. of its length. The current C which
flows round the solenoid and magnetizes the iron, also passes
round the fixed coils of a sensitive electrodynamometer. A se-
condary coil of n turns is wound over the iron and is connected in
series with the suspended coil of the electrodynamometer, the
resistance of the secondary circuit being R. When the primary
current C changes, the magnetic induction B changes and an
E.M.F. AndB/dt is set up in the secondary circuit. If the time-
constant of the secondary circuit is very small compared with
the time of a complete cycle, the effects of self-induction may be
neglected, and then there is a current y in the secondary circuit
of amount y= fn ae Now the relation between C and H is
R dt™
expressed by H=47NC, so that C=H/47N. Hence, if the
couple experienced by the suspended coil when a current 7, flows
in it and a current 7, flows in the fixed coil is qi, ergs, the couple
experienced by the suspended coil at any instant due to ¢ and + 1s
qcy ergs, supposing that the deflection is not so large that the
value of q is appreciably different to its value in the equilibrium
position. outs
Now if the time of vibration of the moving coil is so great
compared with the time occupied by the double-reversal of the
current that this process may be regarded as completed before the
coil has moved sensibly from its equilibrium position, the angular
momentum acquired by the coil for a single double-reversal of the
primary current is
BOTTA a — dB _ gAn i 9
Ko =| q0yit = {rp HS dt= {oe [HaB ...2),
1—2
4, Mr Searle, A method of measuring the [Nov. 11,
where K is the moment of inertia of the coil and @ its initial
angular velocity. Thus since fHdB=47W we have
NR
Let T be the time of a complete vibration of the coil, @ its
greatest angular displacement or “throw” and 7 the restoring
couple exerted by the suspension per radian of displacement. We
have, by the Conservation of Energy,
Ko with (3).
Initial kinetic energy = Potential energy at extremity of swing,
so that bye A Sos 217) ch Ae AON ROR ER Rr hele 6-3. (4).
Also JP = Bie ve SS eect ae ote Eee (5).
From (4) and (5) we find
Goss
Ko = OF CT ajales el stetelelo\ ele lalalsterevecohoreletelatea=te (6)
Thus from (3) we have
NEnTP
adn (7)
The quantity 7/q 1s easily determined as follows :—
Let currents 7,, 7. flow i the suspended and the fixed coils of
the electrodynamometer respectively and let @ be the observed
steady deflection, then
Gist — COMPLE — Vn i iagese sete aoe (8),
so that nlq = tite/¢.
If there is any appreciable damping the expression must be
multiplied by 1+ 4A, where » is the logarithmic decrement. We
have finally
_ NRT,
~ QrAnd
Thus the “throw” of the coil is proportional to the energy lost
in hysteresis.
It is evident that this affords a very ready means of testing the
hysteresis of iron under different physical conditions for a given
maximum value of H, the magnetic force, for all that has to be
done after the constant of the instrument has once been determined
is to observe (by means of a mirror and lamp and scale) the throw
produced by a single double-reversal of the magnetizing current.
For instance, a steady electric current may be maintained through
the iron and the value of W for each value of this current may be
OCLEEEON) | al eee (9).
1895.] loss of energy in Hysteresis. 5
determined by simple observation of the “throw” in each case.
If it is desired to investigate these effects for a given maximum
value of B, the magnetic induction, the process is a little. more
complicated, because the value of B has to be found by the bal-
listic galvanometer method, and the strength of the magnetizing
current so adjusted on each occasion that the value of B may be
kept constant under the varying conditions imposed upon the iron.
In the electrodynamometer which I have constructed for this
experiment, the suspended coil is a long narrow coil of 120 turns,
about 8 cm. long and 1°5 cm. wide, suspended by a silver wire
woo Inch in diameter. The fixed coils have 500 turns and are
designed so as to fit closely round the suspended coil. With 1285
turns in the secondary coil and with the resistance in the secondary
circuit about 100 ohms, the instrument is sensitive enough to
measure the hysteresis loss in the case of an iron wire ‘02 cm.
in cross section. I have made the instrument sufficiently sensitive
to measure W for so thin a wire with the view of investigating
the effects of tensile and torsional stress upon the hysteresis.
Up to the present (3 Dec. 1895) I have not been able to make
any accurate determinations owing to the fact that I have so far
used an ordinary rocking mercury key for reversing the primary
current. With this key, on breaking contact, the primary current
is stopped very quickly, and when contact is re-established the
current very quickly rises to its full strength, and each of these
changes takes place in a time not very large compared with the
time-constant of the secondary circuit. On account of this the
instrument has given results about 100 °/, too large, as judged by
the value of W obtained by a B-H cycle. When, however, a coil
with a large coefficient of Self-induction was inserted in the
primary circuit so that in spite of the key the primary current
could not vary rapidly, the discrepancy was reduced to about
5 °/,. But I have designed a key (somewhat after the fashion of
Prof. Ewing’s “Sine Function” key) which will allow the current
to be quite gradually reversed, and some preliminary observations
have led me to expect that with this key the instrument may
work quite satisfactorily.
Nove added 18 Dec. 1895. The following method of deter-
mining the constant of the instrument is much more convenient
than that described in the paper. Let a constant current C’ flow
in the primary circuit, and while this current is flowing suddenly
produce a known change P in the number of lines of magnetic
force passing through the secondary circuit. This is conveniently
done by suddenly inverting an “earth inductor” which has been
placed in the secondary circuit. The time-integral of the current
6 Mr Blythe, On the forms of [Nov. 11,
thereby produced in the secondary circuit is P/R, and thus the
initial angular momentum of the suspended coil is
gC’'P
where ’ is the initial angular velocity.
But, if 0 is the “throw” produced, we have by (6) o/o’ = 0/@,
so that by (3) and (10)
Two determinations of C’PN/An@ on two different days
agreed to within ‘5 °/,.
The reversing key mentioned in the paper has been con-
structed and measurements of the hysteresis for a specimen of
steel wire have given results agreeing, within the limits of accu-
racy of the observations, with the values obtained by B-H
cycles. For very soft iron in which the maximum value of dB/dH
is over 8000, and six times its average value, there is still a
difficulty due to self-induction when a single wire about ‘01 cm.’
is tested. But I hope to overcome this difficulty shortly.
G F.C. 8S.
(2) On the forms of cubic surfaces containing 27 real straight
lines. By W. H. Buytue, M.A., Jesus College, Cambridge.
The following account of the transition between the various
forms of these surfaces is a supplement to the paper in Proceed-
ings, vol. VIIL., p. 241.
A simple case of a cubic surface is that of a plane and a right
cone shewn by one figure. Take a solid rectangular block, and
let its upper surface represent the plane in question. Cut a right
cone out of this block, axis vertical, having its vertex in the plane
at a point A. Invert the solid cone, vertex at A. The surfaces of
the solid and hollow cone, and that of the plane, represent a cubic
surface. A straight line can be drawn to cut the surface in three
points. Comparing this diagram (1) with (2) and (3), which are
vertical sections of a cubic surface represented by the general
equation, we see a similarity in form. In the case of (8) the
upper hollow portion is connected with the lower. In passing
from the form (2) to (3) and then from (3) to (2) it is evident that
a “hole” is made, joining the upper to the lower hollow portion.
In the case of a cubic surface having twenty-seven real straight
lines there are three such “holes” or openings.
Fia. I.
Fia. II.
Plate I
TY
Te
Diagram (3).
Diagram (2).
Diagram (1),
nr
Phil. Soc. Proc. 1x. Pi 1.
Geet
Baty
vy
Plate TT
Phil. Soc. Proc. 1x. Pt 1.
1895.] Cubic Surfaces containing 27 real straight lines. 7
Three drawings from photographs of a model shew these
openings, the fourth being a view of the under part. [Plate I.
Figs. I—Iv.]
The lines on the solid upper portion which are the same as
those on the lower hollow portion form a double six, these lines
each pass through one opening.
The lines through each opening form a double six.
_ The lines between each opening and the next form a double
SIX.
Twelve lines pass through two openings namely 17, 23, 13, 19,
fet; 20, 115, 16, 4, 22.
Three lines 8, 18, 27 do not pass through any opening.
One conic node.
Take the lines 1,13; 14,6; 4,11; 22,16; 23,17; 10,2 and let
them move up to one another namely 1 to 13, 14 to 6, &e. so as
to form six lines only r,, r,, ..., 75.
These lines will now all pass through a point, and the opening
through which they go will close up to this point and become a
conic node. We now have 15 mere lines and 6 rays of a conic
node,
Two conic nodes.
If the two conic node rays 73, 7, now coincide, another opening
closes up, namely that through which the double six 4, 22, 11, 16,
19, 9, 25, 5, 7, 26, 21, 12 passes. 73, 7, now coincide to form an
axis A, joining the two conic nodes. The line 27 becomes a
transversal meeting the axis. The lines 19,9; 25,5; 7, 26; 21,
12 coincide by pairs to form four rays of the second conic node
T, Ts, 7, Mo. SIX more lines remain, each of which meets the
transversal, namely 3, 8, 15, 18, 20, 24.
Three conic nodes.
Two rays from each conic node 7, 75; 77, 7 may be made to
coincide. The third opening now becomes a point joined to the
other nodes by axes A,, A;. 3, 20; 15, 24 unite to form ry, 7p
rays of the third node. 8, 18, 27 are the transversals.
Four conic nodes.
The six conic node rays in this case may be made to coincide
by pairs. We then get a fourth conic node caused by the closing
up of the opening at the base of the model. 27, 8, 18 still remain
transversals.
Conic nodes may also have been found by considering the solid
portions between two openings as diminishing in size, we then get
a conical point formed by the meeting of two solid conical portions,
instead of hollow ones.
8 Mr Blythe, On the forms of [Nov. 11,
A case of great interest is that in which one of the tangent
planes to the surface is at an infinite distance.
The general equation in Cartesians is
xyz = Aa? + By? + CP + 2Fx+ 2Gy + 2Hz+ K.
The sections parallel to the coordinate planes are conics.
Four of these sections in each case become pairs of straight
lines and two are parabolas. It is clear that we get twenty-seven
straight lines, namely three sets of four pairs together with three
at infinity. '
Examining the meaning of this as regards the model we find
that the three openings become infinitely elongated, we therefore
get a central solid joined to four infinite solid conical shaped
branches. These are so placed that a plane cannot cut both the
central solid and the four branches at the same time.
A correct idea of the shape of this model may be obtained by
placing four cones with their vertices at the angular points of a
tetrahedron, their axes being in the line joining these points to
the centre of the tetrahedron. If this construction be made in
wood or wire it can be covered over with wax or plaster of Paris to
shew the surface exactly.
If the equation is
ayz= Ax + By+C2+4+K,
we still get four sections parallel to the coordinate planes contain-
ing straight lines, but in each case two pairs consist of parallel
straight lines and the parabolic sections do not appear, for they
have coincided with them.
The symmetrical surface mentioned by Mr H. M. Taylor having
four conical points, the equation to which is
e+y+ 2+ 2eyz—-1=0,
is here given. [Plate II.]
A, B, C, D are the conical points and are angular points of a
regular tetrahedron. a, b, ¢ are the middle points of BC, CA, AB.
If we put 2, y, or z=0 we get circular sections, each bisecting four
edges of ABCD.
Portions of these are shewn passing through a, b; 6, ¢; ¢, a.
Next the curve passing through A and a is a parabola which
also goes through D, having its vertex at a.
All sections at right angles to this parabola (that are also
parallel to AD) are conics, and the extremities of their minor or
major axes are upon it.
There is another parabola passing through B, CU and the middle
point of AD at right angles to this one, and is such that if the
major axis of a section has its extremities on the first parabola,
the extremities of its minor axis are on the second.
—~
1895.] Cubic Surfaces containing 27 real straight lines. 9
When looking at the diagram we see that a parabola (e.g. that
through D, a, A) being visible on the face ABC passes through
the point A, and being now on the further side of the solid branch
at A passes out of sight. On each solid branch there are evidently
three edges of the tetrahedron and three parabolas symmetrically
placed, and if we cut any solid branch transversally by a plane at
right angles to the line passing through its vertex and the centre of
the tetrahedron we obtain a symmetrical cubic oval, a diagram
of which is given, having its points of maximum and minimum
curvature at M and m, where the edges and parabolas respectively
meet it. There are also three infinite branches caused by the
section of the plane and the three other solid portions.
Kach edge of the tetrahedron coinciding with four straight
lines on the surface and three being at infinity there are still of
course twenty-seven straight lines on the surface.
Some of the simpler cases of binodes yet remain to be con-
sidered that have equations of the form
aby = Képp.
Construction of the surface.
Take a8y= Kéuv as the equation of a cubic surface where
a, B, y, 5, w, v are of the first degree and K constant. Nine of its
twenty-seven straight lines may be at once obtained as the inter-
sections of the planes a, 8, y with 6, uw, v respectively, and if we
take them to be represented by the numbers 4, 2, 12, 13, 14,
15, 9, 8, 7 the planes and their intersections are shewn by the
scheme
’ ey | a B 9/
eng heal ala
w| 2, 14, 8,
pr ee PS
If we take the lines forming a diagonal of this table, e.g. 4, 14,
7, we can find three straight lines on the surface that meet all of
these, and no more.
By interchanging rows and columns we get in all six such
diagonals. Therefore there are 18 beside the 9 at first found,
making a total of 27.
We can take it that
5, 16, 17 meet: 4, 14; 7. 6, 26, 27 meet 4, 8, 15.
LO 1S. 19 (ot pp dse 8: 12. ea ena Bay ee
PZ ZL) en, Oi 2G, LS. Wie 2a W105, Oy Ae
10 Mr Blythe, On the forms of [Nov. 11,
Take areal coordinates, the tetrahedron of reference being
that formed by the planes a, 8, y, 6; and let
w=(Lat+m,8 —y)n + 6,
vp = (la + mB —) n. + 4.
Let the lines 4,9, 13 form an isosceles right-angled triangle,
hypotenuse in 9. The planes 4, 12, 2 and 13, 14, 15 are per-
pendicular to 4, 9, 13.
15 cuts the edge 18 in the ratio /, : 1,
14 ei 13 jeans
2s 5 4 Bs Ta
12 ‘ 4 ee Ws cask,
If y=0 cut a=0, B=0 at a distance d, above 6=0, and 14, 2
and 12,15 meet a=0, 8=0 at distances d, and d; above 6 = 0, then
% (d, iz d,) = d.,
Nz (ad; — d,) = ds.
We see therefore that by taking arbitrary positions for nine of
the straight lines we determine all the constants in the equation
aBy = Kdouv, except K.
Take a point 0, 8,, y,, 0 on the straight lme 4. Denote the
ratio y, : 8, by p, we shall find that
Nie — ON ANG ee Ny —
will reduce to two independent equations both satisfied by 0, B,,
Yi» 0 if
Ay =m (m oa P),
Ns P= Ta (Mg Ps ee ene eee (A).
and Ay (Mg. — pp) = — Ny Ny (1, mz — 1, p)
These two equations will represent a straight line on the
surface if \,A,A;a8y = duv coincide with aBy= Kody, that is if
rahe ke
If K be known it is evident that using this equation with (A)
we get a cubic equation for p.
When p is determined we get but one value of Aj, As, A; for
each value of p, and thus obtain three definite straight lines on the
surface.
If, however, we consider K as unknown, and take an arbitrary
value for p, say p,, we find K from the equation
Pi (Msy — 14,91) = — Kn?n.? (mM, — pr) (m2 — pr) (am — 1201),
and the other values of p from the quadratic
(Lm, — 1,p) (ms — p) (m1 — p) _ (argh, — Mp) p
(2,m.—1,p1) (Mz — pr) (M,— pi) (MyN2— Nps) pr’
obtained after simplification and division by p — py.
1895.] Cubic Surfaces containing 27 real straight lines. ll
In this case take as an arbitrary point that at which 16 meets
4, we get a quadratic which determines the points at which 5 and
17 meet 4.
Similarly all the other lines may be found.
When the position of all the lines is fixed, the form of the sur-
face can be found by taking sections through any straight line on
the surface.
These sections are conics, the straight line forming part of the
complete cubic section. Many points on these conics are known
as being the intersection of the planes with lines already found.
The rules for the geometrical construction given in Vol. VIIL.,
Pt. iv., page 241 may be deduced from the analytical method given
above. For it has been shewn that the position of the lines 4, 12,
2, 13, 14, 15, 9, 7, 8, and the point at which 16 meets 4 may be
placed in arbitrary positions, and that this construction determines
all necessary constants.
When this has been done the facts used to determine the
remaining lines are
(1) If three straight lines form a triangle this triangle is a
section of the surface.
(2) Any two triangular sections meet each other in three
points in one straight line, e.g. 3,5, 7 and 13, 14, 15 are sections,
3 meets 15, 5 meets 14, 7 meets 15, and the three points of inter-
section are in one straight line.
(8) If we find four points on the surface in one straight line,
this line lies wholly on the surface.
(3). Hapansion produced by Electric Discharge. By Miss
MARTIN.
Acting under Professor J. J. Thomson’s directions, I have
lately endeavoured to find some explanation of certain pheno-
mena first mentioned, I believe, by Herr G. Meissner (ADA. d.
Gesell. der Wissensch. zu Gott. 1871, Bd. xvi. p. 98). In the course
of some experiments “iiber die elektrische Ozonerzeugung und
iiber die Influenz-Elektricitiit auf Nicht-Leitern,’ Meissner ob-
served that if a gas contained in a space between the plates
of a condenser were subjected to a sudden rise or fall of potential
the volume of the gas underwent a momentary increase. His
apparatus consisted of two concentric glass tubes about 50 cm.
long, both rounded off at the lower end and having no connection
with each other in any way except that the inner tube was held
in place at the upper end bya ring of wax. Between the two
tubes was a space of 3—5 mm. The outer surface of the outer
tube, and the inner surface of the inner were coated with tinfoil
12 Miss Martin, Expansion produced [Nov. 11,
having an area of 264 sq. cm. and 136 sq. cm. respectively. Be-
tween the two coatings there was—making allowance for the
thickness of the tube walls—a space of 6—7 mm. Attached to
the outer tube was a gauge to mark the variations of pressure
in the gas under observation.
Having tried various modifications of Meissner’s apparatus with
no very satisfactory results, it seemed advisable to have his appa-
ratus exactly copied—which was easily done as he gives very
clear and careful measurements and descriptions. This was
accordingly done, the only difference being that instead of the
gauge used by Meissner a horizontal tube provided with a small
quantity of sulphuric acid was used.
Observations with this led to the belief that, very frequently
at all events, the movement of the acid in the gauge was accom-
panied by a luminous discharge through the tube due to induction,
Before it could be ascertained if this was invariably the case the
outer tube was accidentally broken and it seemed advisable to
have the new one made of rather different dimensions. Accord-
ingly a piece of tubing about 40 cm. long and having an outside
diameter of 3°3 cm. was used for the outer tube whilst the same
tube as before (57 cm. long, outside diameter 1:2 cm.) was again
used for the inside. Instead of sealing up the lower end of the
outer tube as before, this was now bent and drawn out to serve as
a gauge and provided with a tap to cut off the acid from the
1895.] by Electric Discharge. 13
tube when the latter was being exhausted and refilled with what-
ever gas might be under observation; for this purpose a short
tube projected between the tap and the bend which communicated
with a pump and with the source of gas employed. In this case
the inner and outer tube, instead of being cemented together with
wax, were provided with a rather loose ring of india-rubber be-
tween which and the glass melted paraffin was poured and allowed
to harden so that the joint was air-tight. For about 15 cm.
below the india-rubber the space between the two tubes was
completely filled with paraffin. Instead of lining the inside tube
with tinfoil it was filled with mercury; the outer tube as before
being coated with tinfoil in which spaces were cut to enable the
observer to note what went on inside the tube. This outer tinfoil
which extended from just below the lower end of the paraffin
stopper to within 4 cm. of the bend was 28 cm. long and had
an area of 290°3 sq. cm.—not allowing for the small spaces cut out
—the effective mercury surface of the inner tube was 87-96 sq. cm.
The two surfaces were distant from one another 1°15 cm. and the
air space between the two tubes had a width of ‘9cm. The two
latter measurements may not be perfectly correct as of course
it is the smallest distance between the two tubes that is required
and, though every care was taken, the two tubes may not be
perfectly concentric; there may be an error of 1 or even of 1°5 mm.
The condenser thus formed was mounted on a square of glass by
means of a thick band of paraffin. The whole was then enclosed
in a light-tight case so arranged that the lower part of the appa-
ratus forming the gauge projected from an opening beneath, and
provided with an opening in front fitted with a small blackened
tube through which the interior could be observed. A mm. scale
was affixed to the gauge tube. The mercury in the inner tube
was connected to the inner coating of one Leyden jar, the tinfoil
on the outer tube to another jar, the outsides of the two jars being
connected to earth. The maximum charge upon the two tubes
could be regulated by means of the distance between the ter-
minals of the Wimshurst by which the apparatus was charged.
With these arrangements it was easily seen that any move-
ment of the acid in the gauge of not less than ‘25 mm. was
accompanied by a luminous discharge through the space between
the two tubes, but it appeared at first as though smaller move-
ments than this were unaccompanied by any luminosity. Greater
care however proved that this was not the case, but that every
movement of the acid is accompanied by a corresponding lumi-
nosity between the tubes. It requires great care and some
practice however to see this when at its faintest; it is much
easier to perceive the very slightest shake of the acid than
the almost imperceptible luminous discharge which however un-
14 Miss Martin, Expansion produced [Nov. 11,
doubtedly accompanies it. On the other hand no luminous dis-
charge ever occurs without a corresponding movement of the
gauge, and it is only when the sudden change of potential of
the two tubes is sufficient to cause a visible discharge in the
space between them that any alteration in volume of the gas
therein contained is to be observed.
Of course it might be urged that though a luminous discharge
is always accompanied by an increase of volume in the gas the
reverse may not be the case, but that sudden changes of potential
too weak to give any luminous effect may produce a change in
volume which the form of gauge used is not sufficiently sensitive
to note.
I do not think this is the case. In the first place the gauge
is so sensitive that if two fingers be laid against the top of the
outer tube the acid in the gauge below begins to move in from
1” to 1%5 and in 17” moves through a distance of 20 mm. There
is however a much more conclusive proof that the gauge takes
account of every change of volume and that every such change is
accompanied by a luminous discharge through the gas. If the
distance between the terminals of the Wimshurst be so arranged
that the sudden fall of potential caused by the passing of the
spark is sufficiently great to cause luminosity in the space be-
tween the two tubes upon every discharge there 1s always a move-
ment of the acid in the gauge; but when the fall of potential does
not give rise to a luminous discharge there is never the slightest
movement of the acid.
When however the distance between the Wimshurst terminals
is such that the sudden discharge causes sometimes a faint
luminosity through the gas and sometimes none, the gauge some-
times moves and sometimes does not. It would perhaps be more
satisfactory to have a second observer in order to be perfectly
certain that the two effects synchronize, but I do not think there
can be any real doubt upon the matter. For it is possible so
to arrange things that the majority of discharges of the condenser
shall be accompanied by a luminous induction discharge, in which
‘case the acid generally but not always moves; if now the Wims-
hurst terminals be caused to approach very slightly nearer to-
gether so that the maximum charge possible upon the condenser
plates is very slightly decreased, a smaller percentage of the
discharge is accompanied by the luminous appearance in the
tube, and the acid in the gauge moves a correspondingly fewer
number of times.
This is the result of several hundreds of observations. It
is of course only within extremely narrow limits that this un-
certainty as to whether the sudden discharge will or will not
cause the effects under consideration is observable. It seems
1895.] by Electric Discharge. 15
fair to presume that the luminosity and the increase in volume
are strictly simultaneous. If the charge upon the condenser
plates be so increased that two or three luminous induction-
discharges occur before the discharge of the condenser by the
passing of the spark at the Wimshurst, two or three movements
of the gauge are correspondingly observable.
The minimum strength of charge capable of producing these
effects varies slightly on different days according to temperature
and pressure, but roughly speaking, at ordinary temperatures and
pressures the distance between the Wimshurst terminals must
be equal to the distance between the two tubes. That is to say,
in my experience it has never required to be greater, nor have
I been able to obtain any effect if the space between the terminals
were more than 2°3 mm. less than the space between the tubes,
Thus with the first tubes used, distant from each other about
4 mm., a spark 3:°4mm. was the smallest which produced any
effect, whilst with the larger apparatus subsequently used having
an air space = 9 mm. the minimum effective spark varied from 65
to 9 mm. but was generally about 8 mm.
These observations were repeated with carbonic acid and coal
gas but for a long time with no very satisfactory results, both
these gases appearing to give very much the same effects as air—
except of course that the colour of the induction-discharge was
different.
Meissner, however, is so very positive in his assertion that H
gives distinctly smaller, and CO, distinctly greater, effects than
air that I could not but think some essential point must have
been overlooked. The cause for my failure in obtaining these
differences at length became apparent. Meissner seems always to
have first filled his vessels with the gas to be observed and then
to have charged and discharged them. In my arrangements how-
ever it was found more convenient to do the charging and dis-
charging by mechanical means, and the Wimshurst which was
worked by a small motor was turned on at the beginning of the
observations and left to run undisturbed to the end; thus the gas,
which was always admitted gradually into the vessel, was sub-
jected to any chemical effects of the discharge before being put
into communication with the gauge, the top of which had of
course to be kept closed till the vessel was full of gas. Under
these circumstances the three gases used, dried air, carbon dioxide
and coal gas seem to behave practically identically. But if now
the Wimshurst were disconnected whilst the tube was being
exhausted and refilled, it was found that, on connecting it up
again and discharging frequently as before, air underwent a con-
siderable diminution of volume, and whilst this diminution was in
progress sudden changes of potential would produce marked
16 Miss Martin, Expansion, etc. [Nov. 11, 1895.
luminosity and movement of the gauge which after the air had
assumed a steady volume were too weak to have any effect.
Working with the same strength of charge it was found that
coal-gas underwent practically no diminution—in comparison with
air and CO,, that is to say, there was actually a small diminution
most likely due to the presence of a small quantity of air in the
tube—and the discharging of the condenser thus filled was at-
tended with no greater effects than observed at the close of the
observations with air. With CO, the first movements of the
gauge were enormously greater than those obtained with coal
gas and appreciably greater than those noticed with air; and the
time taken by this gas to assume a steady volume was at least
twice as long as that required by air. This steady volume how-
ever having once been reached, the effects of any subsequent dis-
charge were the same as with coal gas or air.
It would therefore seem that any sudden and temporary
splitting up of the molecules of the gas which may take place
under the influence of the induction discharge is more easily and
thoroughly accomplished while any definite chemical change is in
progress. When nothing of this nature is taking place, all gases
seem to behave more or less alike and to require equal forces to
cause any disintegration. It is quite easy to understand how this
may have escaped observation ; for if a vessel of the dimensions
used has been filled with air whilst free from any electric dis-
turbance, it requires about 600 discharges to reduce the air to its
permanent volume when it gives the least movement for a given
fall of potential; and to similarly reduce an equal volume of
carbon dioxide at least 11000 discharges are necessary.
It would seem that the chemical change which produces this
diminution of volume takes place more easily and quickly at low
pressures; for though, as was before remarked, the gas to be
observed was let in slowly, the rate was not nearly so slow as the
above figures would require ; nevertheless the volume was constant
whenever the condenser had been exhausted and refilled whilst
still connected to the Wimshurst.
I should remark that the above phenomena were also ob-
served whenever the apparatus was suddenly charged, but the
great majority of observations were made on the sudden discharge
through the spark at the Wimshurst as this method was found to
be rather more convenient.
1895.] Prof. Hughes, Exhibition of specimen of Travertine. 17
Monday, 25 November, 1895.
PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR.
L. A. BoRRADAILE, B.A., Selwyn College, was elected a Fellow
of the Society.
The following communications were made to the Society :
(1) Lwhibition of a curious specimen of Travertine lining a
wooden pipe. By Professor T. McK. Huaues, M.A., F.R.S.
The interesting specimen exhibited was presented to the
Woodwardian Museum by Mr Benjamin Holgate, of Headingley,
near Leeds, who has furnished me with the following information
respecting it.
It is a deposit of travertine formed inside a rectangular wooden
pipe, used for conveying water from near the surface to the bottom
of a mine under Magnesian Limestone. The wood decayed away and
was entirely removed, leaving on the surface of the travertine the
impression of every detail of the woody structure, so that it looks
more like wood replaced than a cast of the interior surface of the
pipe. Where a rusty nail projected into the travertine some of the
iron scaled off, and the rust stained the deposit for a considerable
distance round it so as to increase the deceptive resemblance to
sawn timber.
Another curious point in this specimen is the manner in which
there is always a tendency to break along what may be called the
miter joints. The deposit is built up in layers parallel to the
inside surfaces of the pipe, and when crystallization is set up,
the crystals are formed at right angles to those surfaces. The
faces of the parallel prisms readily coalesce to form one crystalline
mass, but the faces of the pyramids do not so easily unite, espe-
cially under conditions in which, owing to the continuously reduced
extent of surface, the marginal terminations are imperfectly de-
veloped.
The same phenomenon occurs in iron casting. If the metal
cools against an irregular surface, which would tend to cause crys-
tallization to start from surfaces arranged at various angles to
one another, where the iron crystallized from one surface meets the
iron whose fibres of crystallization have originated from another
differently inclined surface, these two masses will not coalesce,
but a plane of separation will extend some distance into the
body, and be a source of weakness though the exterior may have
been planed down so that the cause is not obvious.
VOL. IX. PT. I. 2
18 Prof. Hughes, On symmetry in Mulberry foliage. [Nov. 25,
In seeking the explanation two facts have to be borne in mind.
First, that where the two masses meet at the miter their direction
of increment does not coincide. And secondly, that the growth
of the crystals is arrested along the margin by the ever-diminishing
surface upon which they are built up.
(2) On symmetry in the foliage of a branch of Mulberry
with asymmetry in the individual leaves. By Professor T. McK.
HucuHes, M.A., F.R.S.
The question of the forms of leaves has often been treated of,
but I do not know whether the particular point to which I now
call attention has been noticed. Looking at the mulberry trees in
the Fellows’ Garden at Christ’s College, I observed that young
branches thrown out from near the base of the trunk are apt to
bear scalloped leaves something like those of a vine. When in the
progress of the growth and development of the branch these
scalloped leaves are replaced by the normal forms, the change does
not take place by the gradual withdrawal of the lobes equally
all along the margin of the leaves, but the inside of the leaf, that
is the side next the branch, first returns to the undivided condi-
tion, while on the outside of the leaf the lobes are still conspicuous.
On one flat twig all the leaves were shaped like gloves, which
had a separate place for the thumb only, the other fingers being
inclosed together in a sort of bag. In this case the thumbs were
all turned outward, and the undivided margin was next the twig.
Some apparent exceptions were found in which a leaf lobed on
the right was found projecting from the left side of a twig, or vice-
versd, but in all these cases, as far as I have been able to observe,
the leaf which appears not to conform to the rule is growing from
a small offshoot of the twig, so that a leaf which is left-handed in
form with reference to the principal twig to which it at first seems
to be attached, is right-handed with reference to the subordinate
twig from which it really grows.
It would thus appear that the symmetry which has been lost
in the individual leaves still exists in the branches, so that the
twig with all its leaves may be regarded from this point of view as
one large leaf lobed on its margin, and therefore only the outside
margin of each individual leaf partakes of this scalloping, that is,
the left side of those on the left of the twig, and the right side of
those on the right of the twig.
1895.] Dr Gaskell, The Origin of Vertebrates. 19
(3) The Origin of Vertebrates. By W. H. Gasket, M.D.,
LL.D., F.R.S., Fellow of Trinity Hall.
The problem of the ancestry of the Vertebrates can be attacked
from the side of the Invertebrates or from that of the Vertebrates.
To my mind the best chance of a successful solution is to be found
in the study of the Vertebrates themselves, and especially of the
variation which has occurred in each organ or group of organs
within the Vertebrate phylum.
The principles upon which I have investigated the problem
are based upon the continuity of the evolutionary process and-
may be stated as follows—
1. Whenever it is possible to state that the variation of an
organ or set of organs within the vertebrate phylum has taken
place in a well-defined direction, then, by tracing that same curve
of variation a step further, we must arrive at the condition of the
organ or set of organs in the immediate ancestor of the Ver-
tebrate.
2. The same principle holds good whether the curve of
variation is an ascending or descending one, i.e. whether the
organ in question is becoming more important and more con-
spicuous as we ascend the vertebrate phylum, e.g. the cerebellum,
or becoming less important and degenerate, e.g. the pineal eye
and ganglion habenule. In this preliminary paper I propose to
give a short sketch of the history of all the most important organs
and tissues which I have investigated up to the present time and
to shew that in the case of all of them the phylogenetic signpost
points directly to the same group of animals, viz. the Limulus and
its congeners, as the ancestor of the Vertebrates. When once the
clue has been found then embryology confirms it and illustrates it;
of itself it is a bad guide but affords an excellent illustration of
what phylogeny teaches.
To illustrate my meaning I will rapidly sketch the downward
path of the central nervous system and point out the conclusions
to which such a study directly leads.
The history of the Vertebrate central nervous system.
The highest vertebrate nervous system possesses large cerebral
hemispheres, a large cerebellum, a small pineal gland, choroid
plexuses which are pushed into the ventricles and a small mem-
branous roof to the IVth ventricle. As we descend the dorsal
part of the brain becomes more and more membranous, the
cerebral hemispheres are more and more confined to the ventral
2—2
20 Dr Gaskell, The Origin of Vertebrates. [Nov. 25,
side and the pallium becomes membranous; the cerebellar hemi-
spheres are seen in Elasmobranchs to be formed by the invasion of
nervous matter over the membranous folds on each side of the
median lobe or worm, and in the Amphibians the whole cerebellum
is reduced to a small band of nervous matter accompanying the
IVth nerve across the dorsal part of the membranous tube ; finally
in Ammoccetes the whole of the dorsal part of the mid and hind-
brain is formed by large membranous folds with the nervous
system lying ventral to this membranous tube; at one place only
is there any crossing of nervous matter to the dorsal side, viz. at
the IVth nerve and commencing cerebellum. We see then that
the phylogeny of the vertebrate central nervous system shows a
distinct tendency towards the separation of the nervous system
into two parts, viz. a non-nervous epithelial tube and a purely
“nervous part; follow that tendency one step further than the
stage reached in Ammoccetes, separate the two entirely and we
find immediately a nervous system placed in the same position
with respect to this epithelial tube as the nervous system of an
Arthropod with respect to the epithelial tube of its alimentary canal;
we see moreover that in the lowest Vertebrate, the Ammoccetes,
the old mouth and esophagus, the old cephalic stomach and
straight intestine are most easily seen and recognised. Further,
in absolute accordance with this gradual and perfect evolution,
is the history of the nervous system apart from its tube, for just
as parts like cerebellum and cerebral hemispheres diminish in size
as we descend, so other parts which are insignificant in the highest
Vertebrates come out more and more conspicuously as we descend.
This is especially true of the ganglia habenule and pineal eye, and
we see that in Ammoccetes the pineal eye is most conspicuous, is
arthropod in type and that the large right ganglion habenule is
its optic ganglion. In fact, as already shown in previous papers,
the central nervous system of Ammoccetes fits in both topo-
graphically, histologically and physiologically with the central
nervous system of an invertebrate such as Limulus or Scorpio.
Embryologically the phylogenetic history of the old alimentary
tube is represented by the formation of the medullary canal with
its external anal opening by means of the neurenteric canal;
while the history of the formation and growth of the nervous
system round this canal is illustrated by the formation of the
cerebral vesicles, the formation of the posterior fissure, and of
the substantia gelatinosa Roland: and of the raphé.
Again, trace downward the formation of the cavity of the
cranium and spinal cord. In the highest Vertebrate a cranium so
filled with nervous matter as to leave its impress on the confining
walls and a spinal cord surrounded by membranes containing the
cerebro-spinal fluid. As we descend, more and more room in the
1895.] Dr Gaskell, The Origin of Vertebrates. 21
cranium, until at last in Ammoccetes a large cranial and spinal
cavity containing a small brain and spinal cord surrounded by a
large mass of peculiar glandular tissue. One step further, enlarge
the extent of this glandular tissue and make it functional and we
find immediately that in position and relative distribution we are
face to face with the old cephalic liver and generative organs of
the Limulus and Scorpio, and that the same gradual evolution
which has explained the nervous system itself gives the same ex-
planation of the peculiar tissue which originally fills up the greater
part of the cranium and is gradually squeezed out of existence as
the brain grows.
This characteristic glandular tissue, the remains of the old
generative glands and liver of the Limulus, is found nowhere else
in the Ammoccetes except in the auditory capsule, where its
presence will be explained later.
The history of the Vertebrate skeletal system.
Passing from the nervous system let us now consider the |
skeletal system.
In the highest Vertebrates a bony skeleton enclosing the
nervous system to which is attached a facial skeleton, a thoracic
skeleton and bones for the extremities. This bony skeleton can
be traced step by step into the bony skeleton of the fishes and
thence into the cartilaginous skeleton, where it is then found to
form a cartilaginous cranium and vertebre from which spring
ventrally a series of cartilaginous bars associated with the branchize
and viscera. Further downwards we can trace the whole system to its
simplest beginning in the Ammoccetes, where we find the cranial
cartilaginous skeleton consists of the basal trabecule, in front of
which are the nasal cartilages, the parachordals with the auditory
capsules and the branchial bars with a cartilaginous continuation
of the parachordals along each side of the notochord. We may
then conclude that the immediate ancestor of the Vertebrates
possessed a simple cartilaginous skeleton consisting of a cartila-
ginous bar on each side of the axis which was in connection with
an auditory capsule, extra-branchial bars and a nasal cartilage.
We can go further than this, for the cartilages in Ammoccetes are
of two kinds, hard and soft, the matrix of the first stains yellow
with picro-carmine, and of the second red, and we find that the
cartilages of the branchial basket-work and of the two disjointed
rods along the notochord are of the soft variety, while the auditory
capsules and trabecule are of the hard variety. Further, when
transformation takes place the new cartilages are all of the hard
variety so that the evidence points to the soft cartilage being older
phylogenetically, a conclusion which is in accordance with Shipley’s
a Dr Gaskell, The Origin of Vertebrates. —[Nov. 25,
observation that the branchial cartilages are the first to be formed
in the Ammoccetes. We may then argue that in the direct
ancestor of the Vertebrate two axial lines of cartilage ought to be
found and from them a series of branchial bars should issue, which
bars should lie external to the branchie. We ought in fact to
find a cartilaginous skeleton exactly of the kind which exists in
Limulus; where the two axial cartilaginous bars are found in the
two entapophysial cartilagimous ligaments of Ray Lankester and
the cartilaginous branchial bars are found in the cartilaginous rods
which spring from each entapophysis into each branchial appendage
as described by Gegenbauer. This is the only true cartilaginous
skeleton of Limulus, for the ento-chondrite is not cartilaginous but
is made up of tendon and muscle like the central tendon of the
diaphragm (as shown by Schimkewitsch); it stains also like tendon
and not like cartilage.
Again, tracing back the histology of the skeletal tissues we see
how bone is formed from cartilage, and that cartilage is by no
means always quite the same in structure. Among the different
kinds we find that the branchial cartilages of Ammoccetes are
quite distinct and different to any found in the higher Ver-
tebrates. Further i Ammoccetes there is in addition to these
cartilages a peculiar fibro-massive tissue, from which according to
Schneider the cartilages arise, called by him muco-cartilage
(Schleim-knorpel or Vor-Knorpel). This tissue-like cartilage gives
a characteristic deep purple stam with thionin. It shows its
ancestral importance by disappearing entirely at transformation,
being either converted into cartilage or invaded by blood and con-
verted into an areolar fat tissue. .
I conclude then that the immediate ancestor of the Vertebrate
possessed branchial cartilages of the structure of those of Ammo-
coetes, which themselves arose from muco-cartilage. In other words
we are again led directly to the branchial cartilages and enta-
pophysial ligaments of Limulus, for their structure is word for word
the same as that of the branchial cartilages of Ammoccetes, they
stain in the same way with thionin, and the cartilage arises from a
fibro-massive tissue which resembles absolutely both histologically
and in its staining deep purple with thionin the muco-cartilage of
Ammoceetes. This muco-cartilage of Limulus is formed from cells
of the chitinogenous layer belonging to the entapophyses, so that
we see not only how the direct agreement of the cartilaginous
skeleton of Limulus with that of Ammoccetes both topographically
and histologically points to the identity of these two skeletal
systems, but also how we thereby obtain striking evidence of the
manner in which the chitinous skeleton of the Invertebrate gave
origin to the cartilaginous skeleton of the Vertebrate.
1895.] Dr Gaskell, The Origin of Vertebrates. 23
The history of the Vertebrate muscular system.
It would take too long to trace out the changes which have
taken place in the arrangement of the voluntary muscles as we
ascend from the fish to man; it is sufficient to say that such a
comparative myology has been largely worked out, with the result
that the voluntary muscular system of Vertebrates falls into two
well-marked groups, viz. the body or somatic muscles and the
muscles connected with the branchize and viscera. This division
is so marked and so characteristic in the cranial region that the
segmentation of the body is looked upon as double, viz. Branchio-
merie and Mesomerie, and the researches of v. Wijhe have shown
that in the head region of Elasmobranchs segmental sets of
well-defined ventral and dorsal plates of mesoblast give rise
to the muscles of the splanchnic or branchial segments and to
those of the somatic segments respectively. Passing to the
Ammoccetes we see these two sets of muscles still more separated
from each other, so that we may conclude that such double seg-
mentation, being more and more conspicuous as we descend, is a
marked characteristic of the immediate ancestor of the Vertebrate.
The importance of this division of the voluntary muscles of the
body into a splanchnic and somatic group is still further increased
by the fact that the nerve supply for these two sets of muscles is
also well defined and separate in the cranial region. Thus we see
that the splanchnic voluntary muscles are innervated by a seg-
mental set of nerves having well-defined cell origins in the central
nervous system, apart from the groups of cells giving origin to the
somatic muscles. These nerves are V,,, VII, IX, X.
Thus we come to the conclusion that the double segmentation
of the body was brought about because the immediate ancestor of
the Vertebrates possessed a double muscular segmentation of which
the ventral segments were connected with the movement of a
branchial and allied apparatus, and that the cells of origin of
this more perfectly segmented part of the body were grouped in
well-defined groups, separate from the cells of origin of the less
perfectly segmented somatic muscles.
Again, we see that the conditions which exist among the Crus-
taceans and Arthropods, as described by Hardy, exactly fulfil the
requirements just mentioned, for he has shown that the well-
marked segmented muscles of the appendages, whether branchiz
bearing or not, are innervated by nerves arising from well-defined
cell groups in the ganglia, quite distinct from the more diffused
cell groups which give origin to the less completely segmented
somatic muscles.
We see, in fact, that just as the consideration of the skeletal
tissues led directly to the conclusion that the branchial bars were
24 Dr Gaskell, The Origin of Vertebrates. [Nov. 25,
derived from the branchial bars of Limulus, so also does the con-
sideration of the muscular system lead to the same conclusion,
viz. that the branchial muscles are derived from the muscles of
the branchial appendages of Limulus, and therefore to the further
conclusion that the Branchiomerie is due to the segmentation of
appendages: in other words, that V,,, VII, IX and X were all
originally appendage nerves; the proof of this will be given
later.
Again, we find that histological considerations point in a
most striking way to the same conclusion: for we find in Verte-
brates that these splanchnic muscles are not of the same struc-
ture as the somatic, and this difference of structure is most
striking, as shown by Schneider, when we reach the lowest
Vertebrate—the Ammoccetes. Here indeed we see the evidence
of its ancestry in that its branchial muscles are to a large extent
composed of tubular fibres such as are found in Invertebrates,
very similar to many found in scorpions, and not found in Verte-
brates. These muscles are as significant a finger-post as the
pineal eye, and show their phylogenetic meaning by disappearing
entirely at transformation.
The history of the respiratory system and of the I[Xth
and Xth nerves.
Perhaps the best known phylogenetic development of any
system in the Vertebrates is that of the respiratory system, for
we can trace the lungs back to the swim bladder and pass from
the air breathing to the gill breathing Vertebrate, and from thence
to the Elasmobranchs with indications of extra-branchial carti-
laginous bars in addition to the mternal cartilaginous bars, until
we reach the oldest known vertebrate respiratory system, that of
Ammoceetes with its extra-branchial cartilaginous basket-work,
and its segmental branchiz dependent from the basket-work into
the large open respiratory chamber. Throughout the water
breathing Vertebrates the innervation is the same, the VIIth nerve
supplying the Ist or hyo-branchial segment, the IXth the second
or lst branchial segment, the Xth the remaining segments and
throughout, even in the highest lung-breathing animals, the
respiratory centre still keeps its primitive position in connection
with the origin of the [Xth and Xth nerves.
In Ammoccetes we find in strict accordance with the arrange-
ment and nature of the branchial cartilages and muscles that the
separate branchize may be considered as paired branchial ap-
pendages hanging suspended into a chamber so as to leave a
narrow slit between opposite pairs for the passage of water and
food. Further, we find that the blood circulates in these branchize
1895.] Dr Gaskell, The Origin of Vertebrates. 25
not by means of capillaries as in the higher Vertebrate, but by
narrow channels caused by the subdivision of a large blood space,
just as in the branchie of Limulus or Scorpio.
The conclusion then is that the ancestor of Vertebrates breathed
by means of lamellar branchial appendages which had united
together so as to form a scorpion-like body surface, and that the
nerves to these appendages were the VIIth, IXth and Xth.
In fact, the method of formation of the scorpion from Limulus
as given by Macleod precisely illustrates the manner in which
a respiratory chamber like that of Ammoccetes may be compared
in the first place with that of Eurypterus, and so with that of
Limulus. To this point I will revert later on.
The history of the thyroid and of the VIIth nerve.
If we compare the ventral surface of Eurypterus with that
of Ammoccetes, we see that the comparison of the branchial seg-
ments with each other does not complete the ventral surface in
either animal, for in each case a triangular projection passes down
in the middle line and separates the Ist three branchial segments
from each other. This projection in the case of Eurypterus is the
middle projection of the operculum, and in the case of Ammoccetes
is a middle plate of muco-cartilage underneath which lies the
thyroid gland.
In all scorpion-like animals the respiratory segments of the
body are terminated anteriorly by the operculum, just as the
operculum is the first of the lamellar appendages of Limulus, and
in all cases the operculum carries the terminations of the gene-
rative organs, while in a great number of cases, as in Eurypterus,
Thelyphonus, Phrynus, the operculum is double, the posterior part
being gill bearing, while the anterior part carries the organs in
connection with the external orifice of the generative organs.
In Ammoccetes we find that the first of the branchial segments
(the hyo-branchial) is not like the rest of the branchial segments,
the gill surface being confined to the posterior part of the segment
while the anterior part of the segment carries on its inner surface
the ciliated groove called by Dohrn the pseudo-branchial groove ;
this groove as is well known passes from the dorsal to the ventral
side and there joins with its fellow of the other side to form the
so-called duct of the thyroid gland; this bilateral gland lying
under the ventral median tongue of muco-cartilage which separates
in so remarkable a manner the cartilaginous basket-work of either
side. In position, then, the segment composed posteriorly of the
hyo-branchial, anteriorly of the ciliated groove and the median
thyroid corresponds exactly to the operculum of Thelyphonus or of
26 Dr Gaskell, The Origin of Vertebrates. [Nov. 25,
Phrynus or of Eurypterus with its anterior genital part and its
posterior branchial part.
Further, the nerve which innervates the hyo-branchial portion
of this segment is the VIIth nerve, and Miss Alcock’ has shown
that a branch of the VIIth passes along near the ciliated groove to
extend ventrally tailwards as far as the thyroid itself extends ; so
that looking upon the whole of this segment as the opercular
segment we see that the VIIth nerve was originally the opercular
nerve just as the [Xth was the nerve of the first branchial appen-
dage and the Xth of the remaining branchial appendages.
The comparison of the thyroid segment of Ammoccetes with
the anterior genital half of the operculum in Eurypterus and
Thelyphonus means, that the thyroid gland must resemble closely
the median part of the genital apparatus lying under the oper-
culum of these latter animals; and indeed the resemblance both
in position and in structure is extraordinarily close.
The thyroid of Ammoceetes consists of a long tube curled up at
its posterior end, that tube containing along the whole of its
length a very peculiar glandular structure which is confined to a
small portion of its wall.
This glandular structure has no alveoli, no ducts, but consists
simply of a column of elongated cells arranged in a wedge-shaped
manner, the apex of the wedge being in the lumen of the tube;
each cell contains a spherical nucleus situated at the very extreme
end of the cell furthest away from the lumen of the tube. Such a
structure is different to any other vertebrate gland, its secretion is
not in any way evident, it certainly does not secrete mucus or take
part in digestion, and it seemed impossible to compare it with any
other known glandular structure.
Looking however at the pictures given by Blanchard of the
genital apparatus of Thelyphonus and Phrynus it is striking to
see how closely in appearance the median part of the genital
mechanism resembles the thyroid gland of Ammoccetes, and upon
cutting sections of the Scorpion (the only material available) I
found under the operculum in the middle line a tube, the walls of
which in one part were thickened by the formation of a gland
with long cells of the same kind as those of the thyroid, the
nucleus being spherical and situated at the very further end of
the cell, and the cells being arranged in wedges so that the
extremities of each group of cells came to a point on the surface of
the inner lining of the tube. This point is marked by a small
round opening in the internal chitinous lining of the tube; these
cells form a column along the whole length of the tube just as
in the thyroid gland, so that the chitinous lining along that column
is perforated by numbers of small round holes.
1 Miss Alcock’s paper ‘‘On the cranial nerves of Ammoccetes”’ is not yet pub-
lished but will appear shortly,
1895.] Dr Gaskell, The Origin of Vertebrates. 27
So characteristic is the structure, so different to anything else,
that I have no hesitation in saying that the thyroid of Ammoccetes
is the same structurally as the thyroid of Scorpio, and therefore
in all probability of Thelyphonus and of Eurypterus. It follows
consequently that the respiratory chamber in Ammoccetes just as
in Scorpio, Eurypterus, Limulus &c. is formed by a series of
branchial lamellar appendages, the most anterior of which is known
as the operculum and was connected with the genital apparatus
as well as with branchie.
Whatever the function of the thyroid may be in Scorpio, in
Thelyphonus &c., it is of so great importance to the Ammoccetes
that it persists until transformation takes place, i.e. until the time of
puberty; then when the animal becomes sexually ripe, it disappears,
being eaten up by phagocytes, the branchial segments come to-
gether in the middle line and nothing remains of the opercular
segment, except the remnants of the thyroid, the hyo-branchial
part of the segment and the embryonic puzzle whether the VIIth
nerve supplies two segments or one. Still throughout the Verte-
brate kingdom the modified thyroid remains to show by the
serious effects following its removal what an important part in
the economy of the body is played by this modified genital gland.
The history of the motor part of the Vth nerve.
This nerve through the whole of the vertebrate class belongs
to the same series as the VIIth, [Xth and Xth, and as we pass
downwards to the fishes, we find that just as the facial nerve was
the nerve belonging to the hyoid segment, so the motor part of
the Vth supplies the muscles of the mandibular segment, and even
as low down as Petromyzon it is still possible to speak of a man-
dibular segment. When however we pass still lower to the
Ammoceetes we find that great changes have taken place at trans-
formation in the muscles supplied by the Vth nerve, and that now
the Vth nerve supplies a series of structures which are directly
comparable with the appendages of Limulus and Eurypterus.
These structures are the velar and tentacular appendages of
Ammoceetes, and they correspond strictly with the locomotor and
tentacular appendages of Eurypterus and so with the locomotor
appendages of Limulus.
The large velar appendage is the least modified, possessing as
it does the arthropod tubular muscles, a blood system of lacunar
blood spaces, a surface covered with a regular scale-like pattern
formed by cuticular nodosities just as in Eurypterus and in
Scorpio, and at its base a serrated gnathite edge guarding on each
side the place where the old mouth came to the surface, and still
acting as a grinder according to Langerhans, or more probably a
28 Dr Gaskell, The Origin of Vertebrates. [Nov. 25,
strainer for the mixed food and mud which the Ammoceetes takes
in to its pharyngeal chamber. The velar appendages have been
further utilized in line with the respiratory appendages to assist
in respiration, their movements being synchronous with the respi-
ratory movements.
The separate part of the Vth nerve which supplies the velum
passes within it from the dorsal to the ventral surface of the animal,
and then, as shown by Miss Alcock, turns abruptly forwards to supply
the large median tentacle, so that this extraordinary course leads
to the direct conclusion that this median tentacle which is really
double constitutes with the velum of each side the true velar
appendages, and that that separate part of the Vth nerve corre-
sponds to the nerve of the large oar appendage of Eurypterus.
Again on each side of the middle line there are in Ammoccetes four
large tentacles each of which possesses a system of muscles, muco-
cartilage and blood spaces precisely similar to the median ventral
tentacle already mentioned. Each of these is supplied, as Miss
Alcock has shown, by a separate branch of the motor part of the
Vth, and each branch is comparable to the branch supplying the
large velar appendage with its median ventral tentacular part.
As might be supposed from what has already been said, all
these tentacles and the velar appendages vanish upon transforma-
tion, and in their place is found the remarkable tongue and suction
apparatus of the Petromyzon.
The very process of transformation of the locomotor appendages
of the Limulus into the tactile and velar appendages of Ammo-
ccetes 1s shown to us by the condition of affairs in Eurypterus,
where these appendages are no longer chelate, but have been
changed into short tactile appendages with the exception of the
last one which acted as an oar appendage. We see how their
basal parts are all hidden by the lower lip or metastoma which is
strictly comparable to the lower lip of Ammocceetes, and how all
the foremost ones are capable of being retracted into the large
hood which is strictly comparable with the large hood or upper lip
of Ammoccetes; let the lower lip grow larger and let the last
appendage follow the example of the others, and we have imme-
diately no longer Eurypterus but Ammoccetes, with the separate
branches of the motor part of the Vth nerve representing the
nerves of the locomotor appendages of Limulus, and so bringing
this nerve into its true position as an appendage nerve with the
VIlth, [Xth and Xth.
1895.] Dr Gaskell, The Origin of Vertebrates. 29
The history of the VIIIth nerve.
Throughout the vertebrate kingdom the auditory apparatus
remains constant in position, varying in structure to the extent
that the cochlea becomes more developed as we pass upwards, yet
throughout a gradual development can be traced from the simple
auditory capsule of the Cyclostomi to the complicated bony and
membranous labyrinths of man; the changes which took place owing
to the passage from water breathing to air breathing animals, the
formation of a membrana tympani with the remarkable history of
the ossicles does not concern the history of the VIIIth nerve. We
see then that the auditory apparatus and the VIIIth nerve arises in
connection with a simple auditory capsule and a special sense nerve
which is situated between the trigeminal and vagus group of
nerves. Going one step further this means that an auditory
apparatus and nerve similar to that of Ammoccetes existed be-
tween the locomotor or thoracic appendages and the branchial or
abdominal appendages of the Eurypterus-like animal from which
the Ammoccetes arose, and when we turn to Limulus we find
exactly in the same position an organ which is the counterpart of
the auditory organ of Ammoccetes. For, situated at the base of
the last large digging appendage—between therefore the locomotor
appendages and the operculum—is found a large hemispherical
organ to which a moveable spatula-like process is attached, known
as the flabellum and called by Ray Lankester an “ epipodite.”
This organ is confined to the base of this limb; it is undoubtedly
a sense organ, being composed mainly of nerves, and an elaborate
arrangement of nerve cells in connection with innumerable fine
hairs, which are thickly embedded in the chitin of the upper
surface of the spatula. By the varying thickness of the chitin
these sense hairs vary with considerable regularity in length, and
when the animal is at rest this sensory surface projects upwards
and backwards into the crack between the thoracic and abdominal
carapaces, so that while the eyes only permit a look out forwards
and sidewards, and the whole animal is lying half buried in the
sand, any vibrations in the water around can still pass through
this open crevice and so reach the sensory surface of this organ.
The structure of this sense organ is of a somewhat similar cha-
racter to that of the lyriform organs described by Gaubert and
supposed to be auditory.
Further, the most striking and complete proof that this sense
organ of Limulus is the same as the auditory capsule of Ammo-
coetes is found in the fact that in each case the nerve is accom-
30 Dr Gaskell, The Origin of Vertebrates. [Nov. 25,
panied into the capsule by a diverticulum of the liver and
generative organ.
In the Limulus the liver and generative organ, which surround
the central nervous system from one end of the body to the other,
do not penetrate into any of the appendages, whether thoracic or
abdominal, with the single exception of the flabellwm.
In the Ammoceetes the peculiar glandular and pigmented tissue
which we have already recognised as the remains of the liver and
generative organ, which surrounds the brain and spinal cord, does
not penetrate into the velar or other appendages with the single
exception of the auditory capsule where it enters with and sur-
rounds the auditory nerve just as in Limulus.
Although this organ is not apparent in Eurypterus, yet we can
see how the VIIIth nerve came into closer relations with the
VIlIth or opercular nerve than with the Vth as in Limulus, when
the scorpions arose from a Limulus-like form; for im the scorpion
we see that a large organ similar in structure to the lyriform
organs, evidently a special sense organ with a nerve of its own,
viz. the pecten, 1s situated in closer relationship to the operculum
than to the thoracic appendages ; so that looking at it superficially
Ray Lankester considers it as the second abdominal appendage.
In reality its nerve leaves the nervous system anteriorly to the
nerve of the operculum, and the pecten therefore belongs to a
segment immediately anterior to the operculum, and is in all
probability simply the -flabellum of Limulus enlarged and pushed
downwards to gain room, its proper metameric position being
shown by the origin of its nerve from the central nervous system
between the opercular and last locomotor appendage nerves. «
In Limulus the auditory apparatus is enclosed in a chitinous
envelope, not yet become cartilaginous, and as already mentioned
the cartilaginous auditory capsule and the trabeculee of Ammoccetes
are more recent formations than the branchial cartilages, which
latter are already found in Limulus.
The history of the cranial segments and nerves.
From what has been said it follows that the mystery of the
vertebrate cranium and cranial nerves is now solved, for we see
that the question of the bony segments can be traced back to
Petromyzon and so to Ammoceetes, with its direct genetic relation-
ship to Eurypterus, and that the cranial nerves are in their origin
the nerves of the prosomatic and mesosomatic appendages of
Eurypterus, and so of Limulus.
We may tabulate them as follows:
1895.] Dr Gaskell, The Origin of Vertebrates. 31
Cranial
nerves Ammoceetes Limulus
I olfactory organ olfactory organ (well
Supra seen in Thelypho-
cesophageal ‘i Pea ee
ganglia op aa , lateral lateral eyes
Il’ pineal eyes median eyes
oa ss t yet ked out
ee ys someon
Vina
| tentacles locomotor appendages
m3
m4
Vins velar appendage last locomotor ap-
Infra pendage
cesophageal | V, corresponding epimeral sensory nerves
and VIII auditory organ flabellum
abdominal | VII, thyroid genital operculum
(foundin Thelyphonus,
gangha | VII, hyo-branchial branchial operculum
| &c., not in Limulus)
IX 1st branchial Ist branchial
ae 2nd 7 2nd ”
X, | 3rd » 3rd ”
Pe th, Sth
The comparison of the sensory part of the Vth with the epi-
meral nerves of Limulus, the meaning of the II[Ird and IVth nerves,
of the sensory branches of the vagus group &c., must be left until
the completion of Miss Alcock’s investigation of the course and
distribution of all the branches of the cranial nerves in Ammoceetes,
and their comparison with the homologous nerves of Limulus and
Scorpio.
Two points of interest may be mentioned here, viz. the genesis
of the medulla oblongata and the reason for the invariable position
of the glossopharyngeal as the separate nerve of the first true
branchial segment.
The comparison between the medulla oblongata of Ammoccetes
and of Limulus shows that in the latter, the only nerve belonging
to the lamellar appendages which arises from the medulla ob-
longata is the nerve of the operculum, ie. the VIIth nerve of
Ammoceetes, the [Xth and Xth nerves arising from the separate
abdominal ganglia; in other words, only one ganglion and nerve
belonging to the abdominal or mesosomatic appendages has
32 Dr Gaskell, The Origin of Vertebrates. [Noy. 25,
travelled up into the thoracic or prosomatic fused mass of ganglia.
In the Scorpions Lankester has shown a further amalgama-
tion in the Scorpionini where the 1st branchial appendage as well
as the genital operculum is innervated from the medulla oblongata;
and yet again a still further amalgamation in the Androctonini
where the two foremost branchial appendages are innervated from
the medulla oblongata.
In fact, we see in the passage of the Crustacean into Limulus,
and Limulus into Scorpio and Androctonus, the same law of gradual
fusion of more and more of the ganglia of the ventral chain to
form the medulla oblongata, until at last all the nerves of the
branchial appendages arise from these fused ganglia, and the
vagus nerves of Ammoceetes result. The same process has con-
tinued onwards into the Vertebrates higher than Ammoccetes with
the result of the inclusion of vertebra and spinal nerves into the
occipital region of the skull as seen in various Elasmobranchs and
Ganoids.
Further, the solitary position of the glossopharyngeal, separated
as it always is from the vagus, is suggestive when we find that in
all the scorpions the nerve to the 2nd gill appendage is taken up
and no more, and that in Thelyphonus and the Pedipalpi generally
there exists only one gill-bearing appendage im addition to the gill-
bearing part of the operculum. In other words, the nerves which
correspond to the glossopharyngeal and facial nerves are in-
variably found in connection with the operculum and a gill-
bearing appendage even when the appendages homologous to
those supplied by the vagus nerve did not carry gills.
The history of the heart and ventral aorte.
Without tracing the modifications of the vascular system
throughout the vertebrate kingdom, it will be sufficient to say
that the simplification which takes place as we pass down to the
Elasmobranchs shows that the heart and conus arteriosus arose
from the subintestinal vein which by dividing into two formed the
two ventral aorte, the main function of which was to send the
blood into the gills for purposes of aeration.
Further, Paul Mayer in his paper on the origin of the heart
and blood vessels in Elasmobranchs, has shown that this appa-
rently single subintestinal vein is in its origin double, and that
therefore in all Vertebrates the heart and ventral aorta arises from
two long veins which are originally situated on each side of the
middle line; by the formation of the head-fold these come together
ventrally, coalesce into a single tube which forms the subintestinal
vein and heart, still remaining double as the two ventral aortz
with their branchial branches into each gill, as is well shown in
1895.] Dr Gaskell, The Origin of Vertebrates. 33
the case of Ammoccetes. The heart, then, of all Vertebrates, unlike
the invertebrate heart, is formed from the coalescence of two main
venous trunks or sinuses situated ventrally, its original purpose
being to send blood into the gills for the purpose of aeration. One
step further leads to the conclusion that these two longitudinal
venous sinuses are the two longitudinal venous collecting sinuses
of Limulus and Scorpio. In both cases they form two large ven-
trally situated blood vessels from which the blood passes to the
gills, and, further, in both cases the walls of these two sinuses are
connected with the pericardium bya system of transparent muscles
described by Milne Edwards and named by Lankester veno-peri-
cardiac muscles.
These muscles are hollow, both near the vein and near the
pericardium, so that the blood in each case fills the cavity, and
as they contract with the heart, that part of them in connection
with the venous collecting sinus already functions, as pomted out
by Milne Edwards and Blanchard, as a branchial heart.
The ventral aorte of Ammoccetes correspond exactly in position
and in function with these two venous collecting sinuses in Scor-
pion, and therefore in Limulus; and we see in Ammoccetes the
position of the original dorsal heart represented by that extra-
ordinary column of peculiar tissue containing fat which is situated
in the middle line between the spinal canal and the surface.
The further relation between the vascular and lymphatic sys-
tems of Ammoccetes and the vascular system of Scorpio to-
gether with the consideration of the pronephros, will be considered
later.
The history of the Alimentary Canal.
The history of the vertebrate alimentary canal is the history of
nature’s great mistake and how she rectified it; for at the time
when Vertebrates were formed, the lines upon which evolution was
working led straight to an increasing antagonism between the
increase of brain power and the sufficient feeding of the organism ;
for the increase of brain power meant the increase of connections
between the supra-cesophageal ganglia and the lower nerve
centres, meant therefore an increase of nervous matter around
the csophagus with the result of diminishing the size of the
cesophagus to such a degree that at first only liquid nourish-
ment could be taken in, and finally the choice lay between
starvation and cessation of growth of brain. In Limulus we
already see the commencement of the struggle, and in the forma-
tion of the Scorpions and Arachnids we see not only how narrow
the cesophagus has become so that the whole class are able only to
take in liquid food—, and indeed in certain Arachnids a special
suction pump arrangement has been devised in their stomachs
VOL. IX. PT. I. 3
34 Dr Gaskell, The Origin of Vertebrates. [Nov. 25,
to get through even liquid food—, but also how with the increasing
brain development the great mass of liver and generative organ
was shifted from the cephalic to the abdominal region, thus bulging
out the ventral surface of the body until it came into contact with
and fused with the lamellar branchial appendages on each side.
In this way the great class of Arachnids was formed, but in
vain as far as further evolution went, for no amount of room
around the brain could prevent the constricting action of the
enlarged cesophageal commissures on the cesophagus. Still among
those Limulus and Scorpion-like forms which were in those days
lords of creation and amongst whom the struggle for existence was
very keen, there were some in which the ventral surface did not
reach up to and fuse with the lamellar appendages, although by the
coming together of these latter a body surface like that of Hurypterus
was formed. In these cases then a respiratory chamber was formed
with gills and gill slits between the fused appendages, then came
the piercing of the operculum so as to put this chamber into
communication with the oral cavity. Such opening of communi-
cation is preserved for us embryologically as the breaking through
of the septum of the stomatodzum, for this septum is in the exact
position of the operculum and has nothing to do with the velar
appendages. In this way then these animals took in water of
respiration through the mouth or gill slits into a chamber formed
by the branchial appendages and with this respiratory water food
of various kinds was naturally taken. Such food could be digested
because as shewn by Miss Alcock the skin of Ammoceetes pours out
a secretion for the purpose of keeping its skin clean, which is easily
capable of digesting fibrin. It appears from Hardy’s researches
that a similar secretion is poured out on the carapace of Daphnia
and other Crustaceans. With the growth of the lower lip or
metastoma and the modification of the basal portion of the last
locomotor appendage, which basal part was inside the lower lip,
into a valvular arrangement like the velum, the animal was able
to close the opening into the respiratory chamber and feed as
blood sucker in the way of the rest of its kind, or when food of the
kind was scarce, keep itself alive by the organic material taken
us respiratory chamber with the muddy water in which it
ived.
In this way then we see how little by little a chamber was formed
by the lamellar branchial appendages which functioned also as a
digestive chamber.
Such I imagine to have been the origin of the respiratory
part of the vertebrate alimentary canal, and the manner of forma-
tion of the rest of the tube is shown to us by the evidence of
phylogeny, embryology and paleontology.
Tracing back the alimentary canal along the Vertebrates we
1895.] Dr Gaskell, The Origin of Vertebrates. 35
find in the highest forms a great length of intestine innervated by
the vagus nerve, between the hind-gut with its innervation from
the sacral region and the fore-gut innervated by the glosso-
pharyngeal and facial as well as by the vagus.
Passing downwards we see the fore-gut becoming branchial still
connected with the hind-gut by a long intestine innervated by the
vagus nerve, but the length of this latter in proportion to the
length of the whole is much less. In fishes the length becomes
smaller and smaller, the tube is straight instead of thrown into
innumerable folds and at last in the Ammoccetes we find a small
intestine innervated by the vagus between the large branchial
fore-gut and smaller hind-gut. In other words, the phylogenetic
history of the vertebrate gut shows that the line of tendency as we
descend the phylum is steadily towards an approximation of the
cranial and sacral portions of the gut: pass one step further and we
should find as in Limulus the end of the branchial chamber close
to the cloacal termination of the gut, i.e. close to the cloacal
termination of the old gut.
In other words, the branchial chamber was continued on as a
short tube which broke through into the old existing cloaca and
the elongation of that tube is the striking fact in the phylogeny
of the vertebrate gut. The formation of this tube from the
respiratory region by the coming together of the ciliated hyper-
and hypo-pharyngeal ridges is well seen in Ammoccetes, and
embryologically the travelling down of the vagus and the fact
of this part of the gut being always supplied by the great branchial
nerve, the vagus, is strong confirmatory evidence that the middle
part of the intestine has arisen in the vertebrate phylum as the
gradual elongation of an originally small junction between the
respiratory chamber and the cloacal region. The evidence of this
junction taking place is preserved for us embryologically by the
breaking through of the septum of the proctodeum just as the
passage from the mouth region to the respiratory chamber through
the operculum is represented by the breaking through of the
septum of the stomatodzum.
Again, the embryological development of the Vertebrate illus-
trates this history in the most striking way, for not only does it
show that the embryo grows in length by additions made between
the head end and the tail end, but also that at a time when the
fore-gut and hind-gut are well formed the mid-gut is still a mass of
yolk ; this is especially well shown in Shipley’s specimens and is a
clear indication that the formation of the mid-gut takes place em-
bryologically and therefore took place phylogenetically much later
than the formation of the fore-gut or hind-gut, for the argument
often used, that yolk retards development and for that reason the
mid-gut is formed latest, is to my mind evasive rather than real,
3—2
—
36 Dr Gaskell, The Origin of Vertebrates. [Nov. 25,
and it seems to me much more probable that the yolk is there
because that part is last formed, than that it is last formed because
the yolk is there.
The paleontological evidence.
It is clear from what has been said that the evidence of
paleontology ought to show, firstly, that the Vertebrates appeared
when the waters of the ocean were peopled with the forefathers of
the Crustacea and Arachnida, and secondly, the earliest fish-like
forms ought to be characterised by the presence of a large cephalic
part to which is attached an insignificant body and tail. Such
was clearly the case, for the earliest fish-hke forms appear in the
midst of and succeeding to the great era of strange proto-
crustacean animals, when the sea swarmed with ‘rilobites,
Eurypterus, Slimonia, Limulus, Pterygotus, Ceratioceras and a
number of other semi-Crustacean and semi-Arachnid creatures ;
and when we examine these ancient fishes we find such forms as
Pteraspis, Ptericthys, Astrolepis, Bothriolepis, Cephalaspis, all
characterised by the enormous disproportion between the extent of
the head region and that of the body. Such forms would have but
small power of locomotion, and further evolution consisted in
gaining greater rapidity and freedom of movement by the elonga-
tion of the abdominal and tail regions, with the result that the
head region became less and less prominent, until finally the
ordinary fish-like form was evolved, in which the head and gills
represent the original head and branchial chamber, and the
flexible body with its lateral line nerve and intestine innervated
by the vagus represent the original smal] tail-like body of such a
form as Ptericthys.
Nay more, the very form of Ptericthys and the nature of its
two large oar-like appendages, which according to Traquair are
hollow like the legs of insects, irresistibly remind one of a form
like Eurypterus in which the remaining appendages had shrunk to
tentacles as in Ammoccetes, but the large oar-like appendage still
remained, coming out between the lower and upper lips and
assisting locomotion. The Ammoceetes-like forms which existed
between the time of Eurypterus and the time of Ptericthys not
having developed bony plates have not yet been found, although
the recent find of Traquair of Paleeospondylus Gunni is exceedingly
interesting in this respect. The evidence of paleontology as far
as it goes confirms absolutely the evidence of anatomy, physiology,
phylogeny and embryology and assists in forming a perfectly consis-
tent and harmonious account of the origin of Vertebrates, the whole
evidence showing how nature made a great mistake, how excellently
she rectified it, and thereby formed the new and mighty kingdom
of the Vertebrata.
1895.] Dr Gaskell, The Origin of Vertebrates. 37
In the discussion which followed, Mr A. SEDGWICK said that:
The arguments used by Dr Gaskell to prove that Vertebrates
are descended from Arthropods might with equal cogency be used
to prove the reverse, viz. that Arthropods are descended from
Vertebrates; Arthropods being quite as highly specialised as
Vertebrates. Further the facts alleged in support of the conten-
tion are of a superficial and unimportant character, and not of
a kind to be brought forward or considered until the more
important and deep-reaching anatomical differences between the
two groups have been reconciled. For instance such important
anatomical matters as the condition of the ccelom, of the nephridia,
of the relation of the blastopore to the neural surface are not even
referred to. Nor is a single embryological fact brought forward
in support of the astounding contention that the alimentary canal
of the Arthropod has been changed into the central nerve-tube
of the Vertebrate.
It was further pointed out that Dr Gaskell’s paper was wanting
in that precision and accuracy of statement required in a specu-
lative investigation of this kind; that it showed internal evidence
suggesting that he did not fully appreciate the relative importance
of anatomical facts, and finally by the use of certain words and
expressions in an erroneous and inaccurate sense it seemed to
show that. Dr Gaskell was ignorant of some of the most important
principles which must underlie all sound and useful phylogenetic
speculation.
Mr MacBripke said that Dr Gaskell had brought forward some
interesting points in the anatomy of Ammoccetes but that no step
in advance had been made in the direction of solving the ques-
tion of Vertebrate ancestry. The objections to be urged against
Dr Gaskell’s theory on this subject were mainly two.
1. The Vertebrates in the fundamental constitution of some
of their most important organs—viz. ccelom excretory organs—
belonged to a much more primitive grade of evolution than the
Arthropods, masmuch as the same general arrangement was
found in the less differentiated members of many quite distinct
phyla, viz. Mollusca, Brachiopoda, Polyzoa, Annelida, &., whereas
the arrangement found in Arthropods was highly specialized.
2. The reasoning Dr Gaskell employed to prove the descent
of Vertebrates from Arthropods was illegitimate. In postulating
changes which they suppose to have occurred in the history of
the race, zoologists confined themselves to those which could be
inferred by comparing together animals of undoubted affinity with
each other.
There was no evidence that fundamentally important organs
such as the alimentary canal could be lost and redeveloped in
another place.
38 Dr Gaskell, The Origin of Vertebrates. [Nov. 25,
If such assumptions were allowed the descent of any animal
from any other could be proved.
Mr 8. F. Harmer pointed out that Dr Gaskell had based his
conclusions on two main lines of argument; the first being the
assumption that the comparative study of any particular organ
within the limits of a single group will not only enable us to
retrace the steps which evolution has taken, but will give some
clue to the conditions which existed prior to the evolution of that
organ as such; and the second being derived from a detailed
comparison of Limulus with Vertebrates.
Instances were given to show that the first assumption is
fallacious. The evolution of the lung may have been retraced to
the simplest form in which that organ exists in Vertebrates, but
it does not follow that the line can be produced backwards so as
to give any indication of the conditions antecedent to the evolu-
tion of the air-bladder. Nor does the retracing of the lime of
evolution of the Perissodactyle hand or foot give any information
with regard to what preceded the pentadactyle condition.
It was admitted that the resemblances between Limulus and
Vertebrates were, on Dr Gaskell’s showing, of a remarkable nature;
but many of the details could be satisfactorily criticized only by
one who has made a special study of both Limulus and the
Ammoccet. It was, however, suggested that since the resem-
blances extended to such minute points of detail, 1t would be
remarkable, if Dr Gaskell’s theory were true, that differences
should exist in what would appear to be fundamental points;
as, for instance, the numerical difference between the branchial
appendages of Lamulus and the branchial bars of Petromyzon.
Dr Gaskell concludes that the fact that the intestine is elon-
gated in the higher Vertebrata and straight in the Ammoccet
points to an original “approximation of the cranial and sacral
portions of the gut”; and that therefore the branchial chamber
formerly terminated close to the cloaca. It would equally well
follow from this line of argument that other groups of animals in
which the intestine of the higher members is convoluted and of
the lower forms straight were also descended from ancestors in
which a secondary alimentary canal had been evolved.
The argument from the position of the yolk in Vertebrate
embryos has no real weight. Dr Gaskell, in dealing with the
Vertebrata, has put a special interpretation on a very general
embryological phenomenon. He has entirely ignored other groups
of animals, in this respect; and he is no more justified in his
conclusion that the embryological evidence indicates a late evolution
of the mid-gut in Vertebrates than he would have been in drawing
a similar inference from the developmental history of Mollusca.
On the motion of Mr H. Gapow the discussion was adjourned.
1895.] Dr Gaskell, The Origin of Vertebrates. 39
Monpbay, December 2, 1895.
PRoFeEssor J. J. THOMSON, PRESIDENT, IN THE CHAIR.
The discussion of Dr GASKELL’sS paper “On the Origin of
Vertebrates” was resumed.
Mr H. Gapow said that Dr Gaskell combines the study of
physiology with that of morphology, the latter not being restricted
to the small branch of ontogenetic research which can be guided
only by the method of comparative anatomy.
Much of the ordnance store of embryologists consists of weapons
which are not those of precision, because at present our knowledge
of their nature and meaning is far from satisfactory; for instance
notochord, neurenteric canal, nervous system, ccelom, metamerism.
Objections to Dr Gaskell’s hypothesis, which are based upon such
features, are very precarious.
The incredulity, which Dr Gaskell’s hypothesis has met with,
is referable to two reasons. First, we were ignorant of the
astonishing number of important anatomical and _ physiological
features to which Dr Gaskell has drawn our attention n Ammo-
ceetes and in Limulus, especially the larval Ammoccetes being
full of revelations. Secondly, we are prejudiced in favour of one
or other hypothetical pedigree of vertebrate descent, although it
is not obvious which are at present the favourites, namely Worms,
Sea Squirts, Sea Anemones or even Sea Urchins.
Anyhow, be Dr Gaskell’s hypothesis right or wrong, he has
stirred up so many morphological questions, which can no longer
be neglected, that work has been cut out for us for many years to
come.
Mr BaTEsoN said that it was difficult to make any criticism
which should adequately express to the minds of those who were
not acquainted with the leading facts of the structure and develop-
ment of animals how impossible it was to entertain Dr Gaskell’s
hypothesis of Vertebrate descent. Several difficulties had already
been spoken of, regarding Amphioxus, the Vertebrate Ccelom,
the Notochord, &c., any of which seemed sufficient disproof. ‘Two
points might perhaps be taken which would make the objections
clearer to those who were not professed zoologists. It was natural
however that these difficulties should appeal most to those whose
zoological studies had taken a wider range.
First regarding the relation of the nervous systems of Arthro-
pods and Vertebrates. Setting apart all phylogenetic speculation
it is known by observation that the central nervous system of a
Vertebrate separates from ectoderm in the middle line of the
dorsal side [of a Vertebrate], that is to say that that nervous system
40 Dr Gaskell, The Origin of Vertebrates. [Dec. 2,
is a piece of the dorsal ectoderm. In the Arthropod it is equally
certain that the nervous system separates from the ectoderm in
the ventral middle line [of the Arthropod], and is therefore a
piece of the ventral ectoderm. Nevertheless Dr Gaskell held
both that the nervous system of the Vertebrate was homologous
with that of the Arthropod, and that it was the dorsal surface
of the Arthropod which corresponded with the dorsal surface of
the Vertebrate. Dr Gaskell had made no attempt to reconcile
the different modes of development in the two cases.
Extraordinary changes of structure and function were postu-
lated by Dr Gaskell. These were supposed to have occurred in
evolution, in the course of lineal descent, by the process of varia-
tion. If anyone would try to conceive these variations taking
place before his eyes, he would realize the difficulties imvolved.
For example if it was alleged that a specimen of Limulus had
been found which had developed a mouth in its operculum, or
a perforation from the space occupied by the branchize leading
into the intestine, or feeding or digesting by means of that space,
or with its nervous system enveloping its alimentary canal, no
one would credit the observation without overwhelming testimony.
But Dr Gaskell assumed that all these things and many others
no less astonishing had occurred as variations. No evidence had
been offered that any such variations or any approach to them
had ever occurred, or even that they were possible.
In the absence of such evidence there was no reason why
Dr Gaskell’s suggestion should be seriously considered at all.
Dr Gaskell had mentioned Pterichthys, Coccosteus, and other
fossil Fishes, hinting that he regarded them as possible links
between Arthropods and Vertebrates: had Dr Gaskell any reason
for supposing that these animals were anything but Fishes in the
strictest sense ?
Mr SHIPLEY said he thought that in attempting to derive
one group of animals from another, certain principles were usually
observed, (1) one of these was that in assuming variations to arise
in an ancestor the amount of change assumed and its direction
should be checked by the kind of variation which is already
known to exist in the various members of the group to which
the ancestor belongs, but although no one could deny that the
members of the Arthropoda varied in almost every possible
direction, none of them varied along the lines laid down by
Dr Gaskell; (11) the amount of variation assumed should be
limited: there was no fact known amongst animals which led
us to believe that they ever lost and redeveloped such funda-
mental organs as the entire alimentary canal, the renal organs
and the reproductive organs, yet this was assumed in Dr Gaskell’s
hypothesis; (111) changes of function can arise when the new
1895.] Dr Gaskell, The Origin of Vertebrates. 41
function coexists, perhaps subordinately, with the primary func-
tion, or coexists in another member of the same group or in one
of its larval forms: the remarkable changes of function assumed
by Dr Gaskell had no such origin; (iv) in any attempt at Phylo-
geny we must observe the “embryological unities”: Dr Gaskell
derives the epiblastic lining of the nervous system from the—in
the main—endodermic lining of the alimentary canal and the
mesoblastic “packing” cells around the vertebrate nerve-tube
—in part—from the endodermic “liver” of the Arthropod: (v) in
Phylogeny we must look at the most elementary of the animals
whose ancestor we seek, yet Dr Gaskell started some way up
the Vertebrate scale and omitted from his consideration the
Amphioxus and the larval Ascidian possibly because he regarded
them as degenerate but the same reasoning which led to a belief
in the degeneracy of these groups has been applied to shew that
the Lamprey is itself degenerate.
The Arthropod characters of which we should expect to find
some trace in a Vertebrate descended from a Limulus-like ancestor
are (1) the cwlom, which in the Arthropod is rudimentary and
replaced by a body cavity of a highly specialized character and
yet the ccelom reappears in the Vertebrate in the most primitive
form, just as it exists in the ancestor of the Arthropods them-
selves; (i1) the chitinous skeleton which dominates the structure
of the Arthropods from one end of the group to the other, is un-
represented in their supposed descendants: in connection with
this it may be pointed out that cilia which with the exception
of the Nematodes, are universally present in all animals but the
Arthropods, have re-appeared in the Vertebrata; (111) the pazred,
segmented limbs of Limulus, which are only represented by sensory
papillz round the mouth or by the branchiz.
The result of the whole hypothesis is that we are asked to
believe (i) that the functional alimentary canal of the Limulus,
with its—in the main—endodermic lining, has become the lining
of the Vertebrate nervous system which is epiblastic in origin ;
(ii) that the endodermic “liver” and the testes of the Arachnoid
ancestor have become the mesoblastic tissue surrounding the
nerve-cord of the Ammoccete; (i11) that the Arachnoid ancestor
has developed an entirely new alimentary canal along its ventral
median line, and that this chitinous-lined tube is completed
ventrally by the fusion of the limbs; (iv) that such of the seg-
mented limbs as are not required for this purpose become minute
sensory papille surrounding the mouth; (v) that the renal organs
of the Arachnoid ancestor degenerate into an appendage of the
brain, the pituitary body; (v1) that part of the tissue representing
the testis of the ancestor is to be found inside the internal ear ;
(vil) that the hemoccel of the Arthropod is again replaced by
— 42 Dr Gaskell, The Origin of Vertebrates. [Dec. 2,
the primitive ccelom which is reduced almost to extinction in
the adult ancestor; (viii) that cilia which are primitive have been
lost in the ancestor and re-acquired in the descendant, whilst the
chitinous coating of the former leaves no trace; (ix) that the
heart has disappeared; (x) that with the exception of a part of
the branchial skeleton, the entire skeleton including the notochord
is a new formation, and so are the kidneys and the generative
organs; the paper before us throws no light upon the question
as to their origin.
Mr E. J. Bres said that the gap between an Arthropod
ancestor and the vertebrates is as great as the gap between the
vertebrates and any other ancestral form hitherto put forward.
In considering Dr Gaskell’s theory it is therefore necessary to
make sure that besides deriving support from resemblances in
anatomy and histology, the theory takes into account the main
distinctions between the hypothetical ancestor and the verte-
brates. Using a table from the most recent authority (Haeckel,
Systematische Phylogenie der Wurbelthiere, p. 12), it appears that
all the valid distinctions drawn between Articulata and Vertebrata
have been dealt with in Dr Gaskell’s paper. As for the remaining
points: (1) the presence of a cuticular layer in vertebrates has
been recognised by Leydig, F. E. Schultze, etc., and demonstrated
to be chitmous by G. Wolff; (2) the structure and mode of deve-
lopment of the notochord throughout the chordates is so uniform
that no distinct clue is given to its origin from any pre-existing
organ in an ancestral form.
Dr GASKELL said in reply—I have listened most carefully
to the arguments brought forward against my theory, and it
seems to me that the most important of them may be summed up
as follows.
“The resemblances and coincidences between the structure of
Ammoceetes on the one hand and of Limulus and Scorpions on
the other which I have brought forward are mere trivialities in com-
parison with the true criteria of what constitutes a Vertebrate, viz.
the presence of a ccelom of a more primitive type than that of an
Arthropod, and the existence of a notochord. These are the two
most important points, and as I have given no explanation of
them, the coincidences which I have pointed out, although inter-
esting, are of no real importance.”
I quite understand that these close resemblances between
similar parts in Limulus and Scorpions and in Ammoccetes are
very unorthodox, but they are certainly not trivial. The argument
reminds me of the commotion made in the orthodox world when
it was first suggested that man and the ape were closely akin ;
1895.] Dr Gaskell, The Origin of Vertebrates. 43
how it was then said by an eminent comparative anatomist—These
coincidences and resemblances between the structure of man and
the ape are merely trivial and have no weight in comparison to
the great fact that man has a hippocampus minor in his brain and
the ape has none—to which was afterwards added—man has an
opponens pollicis and the ape has none.
I venture to compare the argument about the ccelom with that
of the hippocampus minor in the earlier controversy, and just as in
the latter it was shown that the ape did possess a hippocampus
munor so I propose to show, not only that there is no vital differ-
ence between the ccelom of the Vertebrate and that of Limulus or
Scorpio, but also that no stronger evidence could be adduced of the
correctness of my theory than is afforded by this very appeal to
the ccelom.
It is clear that the ccelomic cavities which must be compared
in order to test the truth of my theory are in the case of
the Vertebrate the head cavities of Balfour and in the case of
Limulus the prosomatic and mesosomatic ccelomic cavities, for the
whole strength of my argument is based upon the comparison of
the prosomatic and mesosomatic segments of Limulus with the
cranial segments of Ammoccetes.
Fortunately a recent paper by Kishinouyi on the development
of Limulus allows such a comparison to be made; he not only
shows that the ccelomic cavities in each segment of Limulus are
formed by the splitting of the splanchnopleur and somatopleur in
the same way as in Vertebrates, but also that although each one
of the mesosomatic segments possesses a coelomic cavity, this is not
the case for the prosomatic segments. In these latter the Ist
ccelomic cavity is a large preoral one, common to the segment of
the Ist appendage and all the segments in front of it; the
segments belonging to the 2nd, 3rd and 4th appendages have no
ecelomic cavities formed in them; the 2nd ccelomic cavity belongs
to the segment of the 5th appendage and then each subsequent
segment possesses a ccelomic cavity. Clearly on my theory the
Ist large preoral ccelomic cavity common to the most anterior
segments of Limulus corresponds to the Ist large preoral head
cavity of Balfour and of v. Wijhe. Balfour’s 2nd head cavity is the
mandibular associated especially with the Vth nerve. According
to my view the motor part of the Vth represents the five locomotor
appendages of Limulus, and we see already in Limulus that the
segments corresponding to the three foremost of these appendages
do not form ccelomic cavities. Posteriorly to the segments belong-
ing to the Vth nerve a head cavity is found in each segment in
Elasmobranchs and Ammocetes just as in Limulus, the main
difference between v. Wijhe and Balfour being that according to
the former Balfour's hyoid segment is in reality double.
+4 Dr Gaskell, The Origin of Vertebrates. [Dec. 2,
It is clear that the study of the ccelomic cavities in the head
not only gives no support to the opponents of my theory but like
the corresponding argument of the hippocampus minor affords yet
another extraordinary coincidence, so that I presume that the
resemblances between the head cavities of the Vertebrate and of
Limulus must now be included among the rest of the trivial
coincidences.
Before leaving the consideration of the ccelom, I must say that
I heard to my utter astonishment the statement of both Mr
Macbride and Mr Shipley that my theory was preposterous,
because I made the generative and excretory organs of the
Vertebrate arise de novo. Seeing that I have not said a word
about the origin of the excretory and generative organs of Verte-
brates and have never even dreamt of making them arise de novo, I
cannot understand how such an argument can be used against me.
It is true that I believe that the pituitary gland is simply the
coxal glands of Limulus and Scorpions, but that does not imply, as
Mr Shipley asserts, that the renal organs of the Arachnoid ancestor
degenerate into the pituitary body; for undoubtedly Scorpions
and other Arachnids possess a well-defined renal system known by
the name of the Malpighian tubes.
Then I am told that the Arthropod does not possess a noto-
chord, while the notochord is the great characteristic of the
Vertebrate; and I am asked, Where is the notochord in Limulus ?
Similarly in the old controversy it was asked, Where is the
opponens pollicis in the ape? Just as in the latter case the
opponens pollicis is an attribute of man because he has discarded
the quadripedal method of progression and become a biped, so the
notochord is an attribute of the Vertebrate because it has dis-
carded the old alimentary canal and formed a new one. I had not
intended to discuss the origin of the notochord at present, but as
stress has been laid upon its presence and I have been challenged,
I will simply ask the following questions:—“Do embryologists
consider that the notochord arose as a simple tube of hypoblast
which terminated in the region of the infundibulum and extended
the whole length of the body?” If so, “Is it possible to conceive
of more than one interpretation of the original purpose of an un-
segmented hypoblastic tube in a segmented animal which extends
the length of the body from mouth to anus?” I will also point out
that just as the notochord is formed by the proliferation of cells in
the median line ventral to the nervous system, so later on in the
history of the animal a similar proliferation of cells takes place in
the same region to form the sub-notochordal rod ; and again when
the Ammoccetes transforms into the Petromyzon, yet another
similar proliferation takes place in exactly the same region, but
now confined to the ancient part of the animal, viz. the head
1895.] Dr Gaskell, The Origin of Vertebrates. 45
region; a proliferation which forms a solid rod of cells entirely
occluding the opening from the branchial chamber to the anterior
intestine, and then, by a hollowing out process beginning at the
posterior end, forms ultimately the new gut of the Petromyzon.
Mr Bateson objected that the neural plate of the Arthropod is
derived from the ventral epiblast and the gut is dorsal to it; on
the contrary, in the Vertebrate the central nervous system is
derived from the dorsal epiblast,—including in the term central
nervous system both the nervous layers and the layer of the central
eanal,—and ventral to it is the notochord and vertebrate gut. This
difficulty seems to me more apparent than real; the nerve layer
in the Vertebrate as soon as it can be distinguished is always
found to le ventrally to the layer of epiblast which forms the
central canal. In the middle line of the body, owing to the
absence of the mesoblast layer, the cells which will ultimately form
the notochord and those which form the central nervous system
form a mass of cells which cannot be separated in the earlier
stages. The nerve layer in the Arthropod hes between the ventral
epiblast and the gut, the nerve layer in the Vertebrate lies
between the so-called hypoblast (i.e. the ventral epiblast of the
Arthropod) and the neural canal (i.e. the old gut of the Arthropod).
The new ventral surface of the Vertebrate in the head region is
not formed until the head fold is completed ; before this time
when we watch the vertebrate embryo lying on the yolk, with its
nervous system and central canal formed and its lateral plates of
mesoblast, we are watching the embryonic representation of the
original Limulus-like animal; then when the lateral plates of
mesoblast have grown round and met in the middle line to form
the new ventral surface and the head fold is completed, we are
watching the embryonic representation of the transformation of
the Limulus-like animal into the Scorpion-like ancestor of the
Vertebrates.
Mr Bateson and Mr Shipley object that my theory necessitates
enormous jumps, both in conformation and function ; I feel sure
upon further consideration they will see that this is not so, and
that in fact the main jump is not, as Mr Bateson humorously put
it, the sudden transformation of a Limulus into an Ammoccetes,
but rather the transformation of a Limulus into a Scorpion-like
animal by the meeting of the branchial appendages in the middle
ventral line. My whole argument and the whole of my work show
that Ammocetes is closely allied to a Scorpion-like animal such as
Thelyphonus and Eurypterus, the Limulus-like animal being the
more remote ancestor of all three. Messrs Bateson and Shipley’s
objections therefore are not directed against my theory of the
origin of Vertebrates, but against the current view of the manner
in which Scorpions arose from Limulus-like forms ; a view which
46 Dr Gaskell, The Origin of Vertebrates. [Dec. 2,
is based on Macleod’s observations, and is considered reasonable
and indeed highly probable by all comparative anatomists who
know anything about the subject.
There is on my theory no need to assume any sudden change
of function or of anatomical arrangement; I do not presuppose
any transformation anything like as sudden or as marvellous as
that which takes place under our eyes at the time of transfor- _
mation, when the Ammoccetes becomes a Petromyzon.
Mr Shipley’s difficulties about the absence of cilia and the
presence of chitin in Arthropods do not appear serious, seeing that
the alimentary canal of Daphnia appears to be ciliated according
to Hardy’s paper and also the laminated layer of the skin of
Ammoccetes is histologically exactly the same as an internal
chitinous layer. Finally, in answer to the argument of Mr
Sedgwick and Mr Shipley that Ammoccetes is not the lowest
Vertebrate, that therefore I ought to have compared the Limulus
and Scorpion forms with Amphioxus and the Tunicates, to which
Mr Shipley was careful to add that, if I answered that these were
degenerate vertebrate forms, then he had as good right to call the
lamprey degenerate too, I wish to point out that the whole trans-
formation of the Ammoccetes to the Petromyzon is characterised
by the discarding and throwing away of invertebrate character-
istics and the putting on of a more distinctly vertebrate appear-
ance.
We see how by a process of histolysis, the tubular muscles, the
muco-cartilage, the thyroid gland, the velar, tentacular and
branchial appendages are all destroyed, or utterly changed and
new tissues are formed, the net result of which is not degeneration
but the formation of an animal of a distinctly higher grade,
distinctly more comparable with other vertebrates, as instanced by
the possibility of a direct comparison between the skull of
Petromyzon and that of a tadpole, by the growth of the brain and
the appearance of new nerves such as the hypoglossal, the coming
out of the eyes, and the free swimming fish-hke form. In fact
just as the comparison between the Scorpion-like ancestor and the
Vertebrate is shown in the organs of the larval stage, viz.
in Ammoccetes, so the comparison between the higher Vertebrates
and Ammoccetes is shown by the organs of the adult stage, viz.
Petromyzon. I utterly fail to see any reason for considering the
lamprey as degenerate, and suppose that Mr Shipley is referring
to Dohrn’s overstrained and untenable hypothesis that the lamprey
is a degenerate Elasmobranch. |
On the other hand the nearest allies to the Amphioxus
and the Tunicates are the very Ammoccetes themselves, but
how transformed! in the case of the former, no eyes, no cerebral
hemispheres, no special organs of sense; while in the latter, with
1895.] Dr Gaskell, The Origin of Vertebrates. 4.7
the degeneration of the central nervous system, the adult animal
-has degenerated into an alimentary bag with almost all its
vertebrate characteristics gone. It would almost seem as though
in the minds of my opponents the ego of each individual is to be
looked for in his alimentary canal and not in his brain, whereas the
one certain rule in Nature’s law of Evolution may be summed up
as follows—If you want to rise in this world you must get more
brains.
Bitte ann, "Rye ot
ae oto ene
aera ie ine ante 1 hi Be
ee ae cee 4 Hitt efit
eet ae
barat ae ey ar Ape he es
PROCEEDINGS
OF THE
Cambridge Philosophical Society.
Monday, 27 January 1896.
ProFEessor G. D. LIVEING, VICE-PRESIDENT, IN THE CHAIR.
The following communications were made to the Society :
(1) Longitudinal Electric Waves, and Réntgen’s X Rays. By
J.J. THOMSON, M.A., F.R.S.
In the theory of Electric Waves given by Maxwell the only
currents considered are (1) displacement or dielectric currents, and
(2) conduction currents; the first of these is proportional to the
differential coefficient of the electric intensity with respect to the
time, while the second is directly proportional to the electric
intensity itself, When we confine our attention to these currents
Maxwell’s investigation shows that both the electric intensity and
the magnetic force are in the wave front. There is thus no
longitudinal wave, and X, Y, Z the components of the electric
intensity satisfy the condition
d ne dY dZ
— 1 + +} =0;
dt (dx dy dz
this, which expresses that the volume density of the electrification
remains constant, is the condition that there should be no longi-
tudinal wave. Now though the dielectric and conduction currents
leave the volume density of the electrification unaltered, there is
a third class of currents, not considered by Maxwell, which may
alter the volume density of the electrification; these are convec-
tion currents, i.e. currents due to the motion of electrified bodies
through the ether or of the ether past electrified bodies. When
these currents exist the condition for the vanishing of the longi-
tudinal wave is not satisfied, and in fact in this case we may
evidently have longitudinal waves. Thus we know that in a
vacuum tube the electrification has a finite value in certain parts
VOL. IX. PT. IL. 4
50 Professor Thomson, Longitudinal Electric Waves, [Jan. 27,
of the tube, and that the charges producing this electrification
can move about, and by so doing produce a convection current.
Let us suppose, for example, that we have a vacuum tube, and
that in this tube all the atoms of the gas which are charged at all
are charged with electricity of the same sign and move with a
velocity p parallel to the axis of the tube, let the electric intensity
be parallel to this axis and equal to X, let K be the specific induc-
tive capacity of the medium in the tube, p the volume density of
the electrification. Thus in this tube there is a dielectric current
equal to
and a convection current equal to
1d
pp =P 4 Gg, (KX);
the total current parallel to the tube is thus
d (K ie ad
Fi lig Ett? ie ag EX
and this must be the same at all parts of the tube. For if wu, v, w
are components of the total current
du dv. dw
and in this case V—0, 0 — 0.
Hence we have
¢ (KX) +p © (KX) =f,
where / (¢) represents a function of the time.
The solution of this is
Kee i f(t) dt + F (w — pb),
where F’ denotes an arbitrary function of «—pt. This represents
a longitudinal wave of electric intensity, travelling with the
velocity p: the velocity of translation of the electrified atoms.
When, as in the case of a vacuum tube, we have free charged
atoms present the existence of convection currents is quite obvious.
The following considerations show that such currents may, how-
ever, occur in a solid dielectric, with all its molecules intact, pro-
vided each molecule consists of a positively electrified atom paired
with a negatively electrified one. For though in this case p
will vanish if we take its value over a space enclosing a large
number of molecules, yet if we are dealing with phenomena
a
1896.] and Réntgen’s X Rays. 51
involving lengths comparable with the size of a molecule, if we are,
for example, considering waves whose wave lengths are comparable
with molecular distances, it is evident that we cannot assume that
pis zero; we must regard p as having at each point of space a
finite value which will be given by the equation
d d d
Suppose now that the ether is moving past the molecules with
a velocity whose components are p, qg, 7; or more generally let
~p, 7, r be the components of the ether relative to the molecule,
then this will produce convection currents whose components are
pp, gp, rp; these convection currents will give rise to longitudinal
waves.
‘Thus in this case the conditions for the production of such
waves are (1) that we should have some means of producing waves
whose length is comparable with molecular distances, (2) that we
should be able to set the ether in motion.
Now it follows from the laws of electrodynamics that if we
regard the ether as a perfect fluid the pressure due to which is
equal in all directions, then it must in general be set in motion
when changes are occurring in an electric field. For each unit
volume in the electric field possesses a momentum whose com-
ponents are
K K K
= {Zb — Yc}, ig Xe 4a}, ae {Yb— Xa},
where K is the specific inductive capacity, X, Y, Z the components
of the electric intensity, a, b, c the components of the magnetic
induction. Let U, V, W denote the differential coefficients of
these three quantities with respect to the time. Then a force
having the components U, V, W must act on each unit volume of
the field. This force will set the ether in motion unless it can be
balanced by the pressure due to- the ether, the conditions for this
are, if p is the pressure of the ether,
apis -) dpe iden.
BEng oul viggg a
or
—- = - 6d 0:08:42):
unless conditions (a) are satisfied the ether will be set in motion.
These conditions are not, however, satisfied in general when the
electric field is changing; they are not, for example, satisfied in the
field produced by the ordinary dumb-bell vibrator. Thus a vary-
ing electric field will in general set the ether in motion, and thus
fulfil requirement (2) for the production of longitudinal electric
4—2
52 Professor Thomson, Longitudinal Electric Waves, [Jan. pari
waves; thus if there were any centre of disturbance to generate
waves whose length is comparable with molecular dimensions
longitudinal waves will spread through the dielectrics in the
variable field.
Before proceeding to discuss mathematically the laws of pro-
pagation of these waves it may be of advantage to state some
of their peculiarities. We shall call the longitudinal waves due
to the motion of the charged atoms in a vacuum tube convective
waves, those due to the motion of the ether through a dielectric,
longitudinal dielectric waves; these second waves might exist m
a vacuum tube along with the convective waves. In the first
place we notice that each of these classes of waves requires for its
propagation the presence of matter carrying electric charges as
well as ether ; longitudinal waves could not on Maxwell’s theory be
propagated through pure ether. The wave length of the convec-
tive waves is not limited, while longitudinal dielectric waves can
only be transmitted when their wave lengths are comparable with
molecular dimension, and therefore are exceedingly small com-
pared with the lengths of the visible and ultra violet rays; the
finer the structure of the dielectric the more limited the range of
waves that can get through. The velocity of propagation of the
convective waves is equal to the velocity of translation of the
charged atoms, while that of the longitudinal dielectric waves is
equal to the velocity of the ether through the dielectric, this
velocity will depend upon the strength of the varying electric field
being larger in strong fields than in weak. If the ether moves
freely through the dielectric then its velocity will not change
abruptly in passing from one medium to another. Neither of
these waves produce any magnetic effects if they travel in the one
case in the direction of the moving atoms, in the second case in
that of the moving ether.
We shall now proceed to find the equations which hold when
convective currents are present in the medium.
We shall begin with the case of convective waves where the
convective currents are carried by moving charged atoms, and we
shall begin with the case when all the charged atoms, whatever
the sign of their charges, are moving with the same velocity: let
p,q, 7 denote the components of this velocity, X, Y, Z the com-
ponents of the electric intensity, a, 8, y the components of the
magnetic force; uw, v, w the components of the total current, K the
specific inductive capacity of the medium, and yp its magnetic
permeability.
Then p, the volume density of the electrification, is given by the
equation
d d , d
Amp =F {KX } a {KY} Rae {KZ}.
1896.] and Réntgen’s X Rays. 53
The convection current has for components
Pp, YP, Tp.
Hence
d /(K d/(K fie
u=4,(—-X)+pp, v= 5(7-¥) +0, w= 9, (q, 4) +7
_dy dB
But ea are fe.’
as dy dZ ay. dB _adX dz
Gey ada de de
Hence we have
d(d/K 1 . d/jdX adY dZ
ila) + pe} =p l\WX-a(Z ie eh
with similar equations for Y and Z.
By differentiating the equation for X with respect to a, that
for Y with respect to y, that for Z with respect to z and adding, we
get
d (dp _ dp dp _ dp) _
di ete tage + 7} =9.
This equation merely represents that the changes in the
volume of electrification at any point is due to the motion of the
charged atoms into or away from the small volume surrounding
the point.
To consider the case of a plane wave put
X =A sin = (wt — (lz + my +nz)),
Y=Bsin i (wt — (lv + my + nz)),
Z = C sin = (at — (la + my + n2)).
And substitute in equations 1, we get
A (o* Zz) = (1A + mB + nC) (wp 2 -z):
B G ia) =(1A + mB + nC) (og == a
eh a speek
C (© = =z) =(1A +mB+ nC) (wr a
54 Professor Thomson, Longitudinal Electric Waves, [Jan. Ts
Eliminating A, B, C we find two values for o, the first is given
by the equation »?=1/uK which corresponds to the transverse
waves as in this case 1A + mB+4+nC=0; the second by the equa-
tion
w= pl+qm+rn.
This represents a longitudinal wave propagated with the
velocity
pl+qm+rn.
We see that
x Y Z
so that unless
DG ae Ai ae
ie. unless the direction of propagation of the wave is parallel to
the direction in which the particles are moving the electric
intensity is not at right angles to the wave front.
We see from these equations that a longitudinal wave of
electric intensity parallel to a fixed direction, say x, can be propa-
gated by a medium containing moving charged atoms even though
the velocity of these atoms is not parallel to «. Thus suppose the
wave of electric intensity parallel to « is being propagated by the
atoms moving with a velocity whose components parallel to a, y, z
are p, qg, 0, then since Y=0, Z=0 we have n=0, m= = , where
V is the velocity of the transverse electrical waves through the ether.
Thus the wave front is not at right angles either to the direction
of motion of the charged atoms or to that of the electric intensity.
If the velocity of the charged atoms is small compared with the
velocity of light m will be small, 7 nearly unity, hence m =
approximately. Now m is the angle which the normal to wave
front when q is finite makes with the direction of the electric
intensity. Hence this angle varies as the square of the ratio of
the velocity of the atoms to the velocity of light. The angular
deflection of the front of the waves produced by a transverse
velocity imparted to the atoms would be almost infinitesimal
compared with the deflection of the atoms themselves.
When the charged atoms move in a magnetic field they are
deflected from their rectilinear course, so that as the preceding
investigation shows a wave in which the electric intensity is
parallel to a fixed direction would be deflected, but the deflection
would be infinitesimal compared with those produced by the
magnetic field on the cathode rays.
1896.] and Roéntgen’s X Rays. 55
We see from equation (2) that if we neglect the square of the
ratio of the velocity of the atoms to that of light we have
ee ae
EL Sines on
>
so that to this approximation the direction of propagation of the
wave coincides with the direction of the electric intensity ; in this
case there is no magnetic force propagated with the wave.
An interesting case of these convective waves 1s afforded by
the problem of a column of air moving like a wind and carrying
along with it both positively and negatively electrified atoms.
Some experiments by Hertz (Wied. Ann. 19, p. 78, 1883) seem to
indicate that something of this nature exists in the neighbourhood
of the positive electrode.
Let us consider the simple case when the velocity (uw) of the
column of gas as well as the electric intensity X is parallel to the
axis of a.
In this case the dielectric current is equal to
K dx
Aare dt ©
The convection current is equal to up where p is the density of
the electrification ; we have however
4p — © (KX)=0.
So that the total current, ie. the sum of the dielectric and
convection currents is equal to
K (dX Ley dX
Ac | at da)’
if K is constant. The total current however in this case vanishes,
so that
Now let us consider the case when w depends to some extent
on the intensity of the electric field, let for example
Uspt+ax,
where p is independent of X.
Then equation (1) becomes
dX wee?
Stagg mle Ober rate
56 Professor Thomson, Longitudinal Electric Waves, [J an. 27,
The solution of which is
X= fie — (p+ OX) theses coscanneeeeee (2),
where f(#) denotes an arbitrary function of X.
Let us take a case where initially the volume density of the
electrification is represented by a harmonic function of « so that
so that when ¢= 0,
and hence by (2)
X=0+5 cos m(e—(p + aX) t),
aX __Asinm {w—(p+aX)t}
dz 1—Aatsinm{x—(p+aXx )t}’
We see from this equation that the denominator of this ex-
pression can vanish and thus p become infinite. The earliest time
at which this takes place is given by
thus
1
t= Fa?
_ darcy ane
ghee +(2n+4)—.
The value of dX/dz, which is proportional to the volume
density of the electrification, at the time t = 1/Aa is given by the
equation
dX 2 A sin|m(a—? a)
an ae ; p+aXx\)’
1 —sin}m(«— ae )t
comparing this with the initial value — A sin mX, we see that the
effect of the motion of the air in the neighbourhood of the positive
electrode has been to enormously increase the maximum value of
the density of the negative electrification, while it has diminished
the maximum value of the positive electrification. It has thus
accentuated the difference in the initial state of electrification in
the tube, for all the negative electrification is practically con-
centrated in a series of equidistant spots on the tube, while the
positive electricity is more evenly distributed than it was initially.
This effect, which is represented by equations similar to those
1896.] and Réntgen’s X Rays. bi
which represent the breaking of a sea wave as it rushes into
shallow water, would tend, if there were any inequalities in the
distribution of electrification in the tube to begin with, to accen-
tuate these inequalities, and may possibly show itself in the
sharply defined striations in the positive column.
Normal Waves in a Moving Ether.
We have seen that the ether in a varying electromagnetic field
must in general be moving. Let us consider the differences
between this case and the ether at rest. In the case of insu-
lators with a quiescent ether the dielectric current is proportional
to the rate of increase of the polarization with the time, in this
case there is no ambiguity,—but when the ether is in motion
the rate of increase to which the current is proportional may
either be estimated at a point fixed in space or at a point moving
along with the ether. The phenomena connected with the effect
of the motion of a refracting substance on the velocity of light
passing through it seem on the whole to be in favour of the latter
view. But if this is the case then the motion of the ether
through an electric field im which the electric intensity varies
from point must produce forces which tend to keep the intensity
constant at a point moving with the ether; for example, when the
ether is moving through an electrified plate, forces must be
generated tending to make the electricity leave the plate and
travel along with the ether.
When the ether is at rest the variation of the electric in-
tensity at any point is opposed by all the inertia of the electro-
magnetic field, while when the ether is moving all the influence of
the inertia is on the side of making the electric intensity at a fixed
point vary, the variation being such that the intensity remains
constant in a given portion of the moving ether.
Let us take the simple case when the electric intensity, X,
and the velocity of the ether, p, are each parallel to the axis of X.
Then the dielectric current parallel to x is
tee
=| dt '? da}’
Thus if the ether were moving in a field in which the electric
intensity was constant with respect to the time, but which varied
from place to place, i.e. a field in which dX /dt vanishes, but where
dX /dzx is finite, the motion of the ether would produce a system of
58 Professor Thomson, Longitudinal Electric Waves, [Jan. 27,
currents, and a magnetic field; the establishment of this field
would have to contend against all the inertia of the system. If we
have a part of field where initially dX/dz is finite but varies
rapidly from point to point, regarding dX/dx for simplicity as a
harmonic function of «, let us suppose that the wave length is
comparable with molecular distances: then if the molecule of a
substance consists of a positively and a negatively electrified atom,
the molecules could arrange themselves so as to produce a distri-
bution of dX/dx of the kind considered.
Now if the molecules group themselves so that X keeps con-
stant at a pomt moving along with the ether, there will be no
current, no magnetic field, and no electrokinetic energy. There
consequently will be a tendency for the molecules in the tract of
the moving ether to arrange themselves so as to produce this
result. This alteration in the disposition of the molecules implies
a longitudinal wave of the electric intensity. If the wave length
of the original distribution of # exceeded molecular distances the
molecules would have to split up into atoms to reproduce this
distribution of X, and there will, in consequence of the inertia of
the system, be a tendency for them to do so.
The equations representing the transmission of wave in the
moving ether are as follows:
Using the same notation as on page 52, p, g, r now denoting the
velocity of the moving ether, we have
d d d d\ K
with similar equations for v and w, we have also
_dy dB
A ay >
tr ie Mas aa az ia
ae Pax 1 dy rE) a dz’
d d d d dX dZ
wget Pag tag tae) mae ody:
Hence when p, g, r are independent of 2, y, z we have
d d d d )? Ge 6 Ce a? dé
pK atPastia teal =| erate age (1)
where yes h eMnydZ
WT Gnidia fide
with similar equations for Y and Z.
1896.] and Réntgen’s X Rays. 59
Take the case of a plane wave, when we may put
saintly og = (o — (le + my + nz)),
Y=Bsin =z (@ — (la + my +nz)),
Z=Csin _ (w — (lx + my + nz)),
substituting these values in equation (1) we get
BK {fo —(pl+qm+rn)PA=A-— 1 {lA +mB+4 nC},
LK {ow —(pl+qm+rn)}P? B= B-m{lA+mB + nC},
BK {wo —(pl+qmt+rn)P C=C — n {lA +mB+4+ nC}.
Eliminating A, B, C we find that either
Vuk (@ — (pl +qm+rn)=1,
or wo —(pl+qm+rn)=0.
If we take the first solution, we have
1A+mB+nC=0,
Le. the wave is a transverse wave; while if we take the second
solution, we have
Se
2B e
it ¢_m_n
Dns) Gone Ae
This represents a normal wave, the direction of propagation
coinciding with the direction of the electric intensity, the velocity
of wave propagation is equal to the component of the velocity
of the ether in the direction of the electric intensity. If there is
only the normal wave, then since
av_dX dz_d¥ aX_az
dai dy incdy edz70\ dat ida
the magnetic force will vanish. Since, however,
dX he d Y. dZ
dz dy dz
is not zero throughout the wave, the volume density of the
electrification is not zero; thus the wave could not be propa-
gated through space devoid of matter, nor could the wave be
propagated without dissociation through an insulator unless the
wave length were comparable with molecular distances.
60 Professor Thomson, Longitudinal Electric Waves, (Jan. 27,
We thus see that on the electromagnetic theory normal waves
of very short wave lengths can be propagated if the ether is
moving.
A normal wave in passing from one medium to another would
be deflected if the lines of electric intensity were bent in passing
from one medium to another. At the junction of two media of
different specific inductive capacity the lines of electric intensity
are refracted, being bent away from the normal as they pass from
a medium of small specific inductive capacity to one of large.
In the case of these very short waves there seems, however, no
reason to suppose that the specific inductive capacity of a medium
would differ from unity. For if we regard a molecule as made
up of a positively electrified atom joined to a negatively elec-
trified one, then, just as the magnetic permeability may be re-
garded as due to the setting of molecular magnets under the
influence of the magnetic force the specific inductive capacity
will be due to the setting of these molecules under the influence
of the electric intensity. If now the wave length of the electric
intensity is comparable with the size of a molecule, a molecule
at one part of its length will be acted on by a force tending to
make it set in one way, and at another part of its length by a force
tending to make it set in the opposite way; the resultant effect
therefore will be little or nothing, and the specific inductive capacity
will practically be the same as that of a vacuum.
Quite recently Professor Rontgen has discovered some remark-
able effects which he is inclined to attribute to normal waves.
We do not know enough about the laws governing those new
rays to be able to say whether they could or could not belong to
the type of normal waves we are investigating; we do not even
know at present that they are normal waves at all.
A series of photographs taken by Professor Réntgen’s method
was shown, and a photograph was taken during the meeting of the
Society.
A very noticeable feature in the bulb producing these Réntgen
rays 1s the phosphorescence of the glass of the bulb. I thought it
therefore of interest to try if these rays were generated when the
phosphorescence of the glass was produced by other means than
the discharge from a negative electrode. To do this, I produced a
ring discharge in an electrodeless bulb; this when the pressure
of the gas is very low is accompanied by intense phosphorescence
of the glass. I exposed a photographic plate protected by thick
cardboard for an hour to such a bulb, but without the slightest
effect. I next tried filling the bulb with oxygen, a gas which
is itself made phosphorescent so as to have both the glass and the
gas phosphorescent, but again a photographic plate was not affected
after an hour's exposure.
1896.] and Réntgen’s X Rays. 61
I also tried without success to photograph in this way by the
phosphorescence excited in a screen powdered over with luminous
paint, by the sparks passing between the terminals of a Ruhmkorff
coil placed close to the screen.
It would thus appear that we can have vivid phosphorescence
without any production of these rays.
I next tried whether the negative electrode could excite these
rays without the aid of the walls of the tube. To test this, I
cut a piece off a photographic plate and enclosed it in a small
ebonite box in the tube in such a way that it came between
the negative electrode and the glass; in this case the plate was not
affected.
The next experiment I tried was designed to try if any evidence
as to the transverse or longitudinal nature of these rays could
be obtained by comparing the depth of the shadows cast by two
plates of tourmaline, (1) when the axes were crossed, (2) when
the axes were parallel. Two pairs of plates A and B were used
and a series of photographs were taken; in some the axes of
A crossed, and those of B parallel, while in others the axes of
A were parallel and those of B were crossed. A very considerable
number of photographs were taken, but there was no evidence
of any effect being produced by the relative position of the
AXES.
A series of experiments (which were not completed until
Jan. 29, the day after the paper was read) were made to test
whether a charged electrified plate would retain its charge of
electricity when exposed to these rays: it was found that the inci-
dence of these rays produced a rapid discharge of the electricity
from the plate, whether this was charged with positive or negative
electricity ; the rate of leak was independent of the sign of the
charge. The potential difference used in these experiments was
about 200 volts. An uncharged metallic plate when exposed to
these rays was not sensibly electrified.
I have much pleasure in thanking Mr Everett and Mr Hayles
for the assistance they have given me in these experiments.
(2) The Equilibrium of Isotropic Elastic Solid Shells of
nearly Spherical form. By C. CHREE, Sc.D.
The equations of equilibrium for isotropic elasticity can be
solved approximately in cases where the surface is not exactly but
only nearly spherical by a method which I have applied in the
American Journal of Mathematics, Vol. 16, pp. 299 et seg. In all
the problems solved in the paper referred to, the material was
bounded by a single surface, but it was indicated J. ¢. p. 382, how
the method could be applied to a shell. The present paper deals
62 Dr Chree, The Equilibrium of Isotropic [Jan. 27,
in detail only with a simple case of the shell problem, viz. that in
which the forces consist exclusively of uniform normal pressures,
different over the two surfaces.
The equations to be solved prove to be ultimately identical
with those treated by me in the Society’s Transactions, Vol. Xv.,
p. 351. Attention is mainly directed to the case of a thin shell
whose surfaces are concentric, similar and similarly situated, as
being that of most physical interest.
Let p, p’ denote the uniform pressures, and let the equations
to the two surfaces be
PSO, Ai AEG} Wa hod eee tecece ese (1);
p=b Gere Gt) Sea ee (2)
where ¢ and ¢’ are small quantities whose squares are neglected,
and o; is a surface harmonic of degree 7. For simplicity there is
supposed to be only one harmonic term, but the method obviously
applies, however numerous these terms may be, supposing the sum
of their numerical values small compared to unity.
Referred to the fundamental polar directions r, 0, @ at any
point on the surface (1), the direction cosines of the normal, since
e is neglected, are
do. 4 1 do; ie
“d0’ ~ “snd do’
similar results with e’ written for e apply over (2).
If the shell were truly spherical the complete solution would
consist in the radial displacement
oe (PP ae ea Di: (3)*,
3m — Nn 7p An
1,
where m and n are the elastic constants in the notation of
Thomson and Tait’s Natural Philosophy.
Answering to (3), the dilatation A and the stresses, in the
notation of Todhunter and Pearson’s History, are given by
A = (b%p' — ap) + (m -) (a* — v} ;
os ool ~ op +(> ios PO}, (4.
00 = $6 = =e oP — ap +3() ('-)},
rd =rb = 66 =0
* Cf. Transactions, Vol. xv., p. 343.
1896.] Hlastic Solid Shells of nearly Spherical form. 63
When the surfaces are no longer spherical, but are given by
(1) and (2), the solution (3) is obviously incomplete, and we
require the addition of some terms from the general solution
contained in my paper above referred to in Vol. xv. of the 7rans-
actions. For brevity I shall simply refer by number to the
equations of that paper, distinguishing them by the letter A.
The terms required are the “mixed radial and transverse” of:
degree 7 containing the harmonic o;. For these from (30,), (31,),
(32,,) we have
ea ame Ans,
u a | r (2 43)n >
ef _.(@+1)m+ 2n y
I—-1 7, mt c a—t—2 2
+r Z,—1 3@i—1)n | ee Tp ac (5),
v= a | ign (4+8) m + 2n
meade 2(2i+3)("+1)n *
ae ae (1— 2)m—2n ated
a5 A 7 Z;+ ue 9 (i A 1) in ——s rae 1 r Zips 5)!
ae) dd [same expression as inside square bracket in (6)]
Here it should be noticed Y;, Z;, Y_;,, Zi+ are simply
arbitrary constant multipliers of the harmonic o;, and not them-
selves surface harmonics as in the paper from which the results are
quoted. They are determined presently from the surface condi-
tions. These constants are all of the order ¢ of small quantities ;
the terms containing them will thus be called “subsidiary terms”
when it is desired to distinguish them from the “ principal terms ”
as given by (3).
The contributions of the subsidiary terms to the stresses rr,
r@, rd are given in (33,), (84,), (35,); their contributions to the
other stresses are not required for our present purpose.
As terms of order é are neglected, the surface conditions over
(1) take the form
~ das Bde i 2
eg tamOdee ov Di Perak Boccapes (8),
> do; de dagen ee
cag > sn dda) ese siaisieleleivislele'sie Co)
doiz 1 da; 1 do;
ee sin Odie aed
64 Dr Chree, The Equilibrium of Isotropic [Jan. 27,
The surface equations over (2) are obtained from these by
writing ¢’ for e and p’ for p.
The two equations (9) and (10) lead to such results as
af (O, $) _ 1d 2
cee ae? Ce a
and are really tantamount to but a single equation
a (Gacp)i— 0:
To obtain the values of principal terms over the surface (1) we
must write a (1 + eo;) for r and retain terms containing the first
power of ¢; for instance the contribution to rr of the principal
terms is easily found from (4) to be
ou
ee stacey ce (p' — p).
In the subsidiary terms proceeding from (5), (6) a (7) it
suffices to write a for r. In such an expression as set m7 e776 the
contribution of the subsidiary terms would be of order e and so
is negligible.
Bearing these points in mind, and noticing that the terms
independent of « cut out, it is easy to verify that the surface
conditions take the form :
ah doh
5 Ee ONE eo AM pr
21+3
ahtarah
5 Ee ees (ou yae
2(4¢ —i-3 7 30° y
—2 (4+ 2) na i =73 pat PP) se otertes (11),
a(a+2)m—n —- il) ee
a Y; na’ Z,
ERIS) 8 ran
=I) =D 3
=) eee
a4+2) 3 &
2 nae. =— 5 (PP) ---- (12),
(?—1—3)m+n,, a sn
2+ 3¢i—-1)m+n,_,
fe oF poe
9 (1 ee 30, ;
—2 (0+ 2)nb—*>3 Z_,, = —— ¢ (p—p) ......... (13),
a? — b3
1896.] Elastic Solid Shells of nearly Spherical form. 65
_t@+2)m—n 7, 2-1) ,.,
iG, «ers
(1) m= 1s
ry Ces baal
1 a) Ge '
42 Oa Zin =— 35 pe (p—p’) pocac (14).
These equations are identical with (38,) to (41,) if in the
latter we put
V; = Viiv — 0,
R, = — 27; = 30° e(p — p’)/(e — b’),
fh’, = — 271"; = 30 & (p—p’)/(a’ — b°)
The values of Y;, Z;, Y_;., Z-; in the present problem are
thus given by (68,) to (71,) when the substitutions (15) are made.
To obtain the subsidiary terms in the displacements for the
present problem, all we have to do is to take the results (92,),
(93,) and the corresponding expression for w, and in them replace
R; by 30° ec; (p — p’)/(a’ — 8°),
Ri, , 8a? éo;(p—p')/(a? —b),
(16)
7; 3) aarh : BF €0; (p — p)/(a _ 6°), a eens
Ps, — Sato: (p— pa —B)
A similar substitution in (94,) and (95,) gives the subsidiary
terms in the expressions for the stresses rr, 76.
This substitution is perfectly straightforward, but the results
of it in general a little cumbrous; I propose giving them explicitly
only for the case when
ce“ €)
and h/a = (a —b)/a
is very small.
In this case we make the substitutions (16) in (96,), (97,) and
the corresponding expression for w, putting e’=e. After effecting
the substitutions I have written h for a—b in the terms depending
on o;. Combining the subsidiary terms with the principal term
(3), it will be found that
VOL. IX. PT. II. 5
66 Dr Chree, The Equilibrium of Isotropic [Jan. 27,
ee ae
U=
Wa = Sma Amr?
a » (20? + 21-3) m+n
Wy Ce es) seresy oper aa eeccee (17).
pi coeae i= a) _ el p=p
dé / \sin 6 do h 4n
The subsidiary terms vanish when p’=p. It is obvious in fact
from (11) to (14) that they must do so in any case, irrespective of
the magnitude of (a—b)/a. Along the same radius vector they
are constant, to the present degree of approximation. The varia-
tion of the principal term in wu along a radius vector was considered
in my previous paper (see (13,) &c. writing —p for R, — p’ for FR’).
This variation is important only when (p ~ p’)/p is small, and in
this case the subsidiary terms in e tend to vanish. As our present
object is to examine the significance of these terms it will be
supposed that (p ~ p’)/p is not small. Omitting the small part of
the principal term in w which varies throughout the thickness, we
may write (17) in the form
eae a (p—p’) aloe ih eo; {(20? + 24-3) m+n}
= h 4n FE 4n (3m — 2) d
| ) mae)
4 | C25 oy (sy = _ et (p— Pp’)
| a | sin 6 ddb/ 4nh
where # is Young’s Modulus, 7 Poisson’s ratio.
Remembering the values of the direction cosines of the normal,
we see that (18) is equivalent to the following three displacements:
a displacement — a?(p—p’)/4nh along the normal,
e i ne (p—p)/Eh _,, » radius vector,
eo," (p — p’) {(20? + 20 — 3) m+n}
if i 4n (8m — n)h
along the normal
or radius vector.
Thus to the present degree of approximation the displacement
is along the normal, that is in the line of action of the applied
force, when
G— 0:
The nature of the change produced by the pressures in the
shape of the thin shell is easily found as follows. It will suffice to
treat the outer surface (1), as the results for the inner are of the
same character. Denote the radius vector by prmewlen
ea; = (p —a)/a.
1896.] Elastic Solid Shells of nearly Spherical form. 67
Then we easily find
ulp=C+1@+1)(p—a)(p ogee
pee Le ey, Seen (19),
0/ Baw /(gr 99h) - ote p’)|(Anh)
= 1 (pa—po b?(p—p’)) -
where C=- a | am —n ae ie ,
A displacement
u= Cp,
be it noticed, would simply change the surface into one similar
and similarly situated to itself, and so leave the shape unaltered.
If pressure be applied over the outer surface only, we have
u/p=—C,+¢(¢+1)(p—a@) p/(2hE)............ (20),
where C, is positive and numerically large compared to the other
term on the right. The radius vector is thus everywhere reduced,
and the proportional reduction is above or below the average
according as
p is less or greater than a.
Under the same conditions
ase AT TEED skid
o anh dd?” ~ 4nh sin O Gide eas
The resultant tangential displacement is thus along the
direction in which p increases most rapidly; e.g. in a spheroid the
tangential displacement is along the meridian, being directed
away from the axis of symmetry or towards it according as the
spheroid is oblate or prolate.
(21).
It is thus obvious that pressure on the outer surface tends to
exaggerate the departure of the surface from the truly spherical
form.
If, on the other hand, pressure be applied over the inner surface
only, we have
nif AE d (4-D) (p= Bp hI x iczecwneas (22),
2 SLU i a Lael
° =~ anh db? ~~ nh sin 0 didics > Je ey ee)
where (C, is positive.
Here every radius vector tends to lengthen, but the lengthen-
ing is proportionally least where the radius vector is initially
greatest ; also the tangential displacement is along the direction
in which the radius vector shortens most rapidly. Pressure on the
inner surface thus tends to make the shape more nearly spherical.
5—2
68 Dr Chree, The Equilibrium of certain Shells. [Jan. 27,
In all cases it will be noticed that for a given magnitude in the
maxima values of eo; the importance of the subsidiary term in uw
increases rapidly with 2 It has been tacitly assumed that the
subsidiary terms are relatively small, so that the solution should
not, without further investigation, be applied to cases in which
ei?o; is anywhere comparable to unity.
The effect of the departure from sphericity on the change of
density produced by the pressure is deducible at once from the
value of the dilatation A. For the thin shell we have from (10,)
and (101,), putting in the latter
P,= fh, — R%,
where R;, R; are given by (16),
Say san! é weasel
Kx a®p — b8p Sedo; (p — p’) (24),
7) @=aQG2D i Crenwe >
Thus if p as before be the surface radius vector,
pes: (a*p ie bp’) i 3 (p = a) (p =p) (25)
(m — n/3) (a3 — 6°) (8m—n)h 7 j
Thence in the case either of internal or external pressure, A is
numerically largest—i.e. the change of density of the material is
greatest—in the neighbourhood of the longest radi vectors.
In the case of nearly spherical shells exposed to bodily forces
depending on solid harmonics, or surface forces depending on
surface harmonics, the equations determining the values of the
constant multipliers in the subsidiary terms required are of the
types (36,), (87,) or (88,) to (41,)—the latter including the case
1=0. The quantities on the right-hand sides of these equations,
answering to f,;, T; etc., are deduced in the same way as the
corresponding quantities for nearly spherical solids were deduced
in my paper in the American Journal. The only mathematical
difficulty consists in representing products of spherical harmonics,
and products of their differential coefficients &., as simple spherical
harmonics or differential coefficients of simple spherical harmonics.
The necessary results of this kind for the shell problems analogous
to the single surface problems I treated in the American Journal
already exist there. When the quantities answering to &,, T; &c.
in (36,) to (41,) are known, nothing remains but to substitute
them for R,, T;, &c. in the general formule, such as (91,).
1896.] Mr Hargreaves, Distribution of Solar Radiation, etc. 69
(3) Distribution of Solar Radiation, and its dependence on
Astronomical Elements. By R. Harcreaves, M.A, formerly
Fellow of St John’s College.
(Printed in full in Zransactions, Vol. xvt.)
(A bstract.)
This investigation was undertaken with the object of providing
exact data for the discussion of the influence of changes in certain
astronomical elements on the distribution of solar radiation on the
surface of the earth. It is well known that secular changes of
climate, of such extent as to give rise to the terms Glacial and
Genial epochs, have been attributed by some authors to this
cause. In view therefore of the interest which this question
has for geologists and others, who might be repelled by the
mathematical analysis, this is preceded by a somewhat full
outline, and numerical results are given in connection with each
point.
The paper begins with the expression of the amount of heat
due to the earth in any latitude, on the assumption of a dia-
thermanous atmosphere, by means of a harmonic series which is
carried numerically as far as the term with one quarter of a
year for period. Denoting by H/r? the amount of radiation on
unit-surface in unit-time exposed perpendicularly to the sun’s
rays at distance 7, the element of heat-supply is
@ being the orbital angle of the sun measured from the spring
equinox.
If the orbit of the earth (or any other planet) was circular
@ would be proportional to mean time. The actual conversion
to mean time is given later, but various conclusions can be drawn
from the present form. The constant hf is introduced by the
relation r°d0/dt =h; when a year is unit of time, its value is 27rab.
As the minor axis is dependent on eccentricity, but only varies
within very narrow limits, the effect of this general divisor is
very slight. The coefficients Z,, L,, L, ... are functions of
latitude, and obliquity of the ecliptic, the same for both hemi-
spheres, expressed in finite terms by complete elliptic integrals
of the three kinds, and also in series of zonal harmonics. The
coefficient of the annual variation L, has the simple form
T. :
—~ sin JA SIN €,
. 2
with opposite signs in the two hemispheres.
70 ‘Mr Hargreaves, Distribution of Solar Radiation, [Jan. 27,
On ZL, depends the total annual supply ; with no obliquity
its value is cosd, vanishing at the pole; as the obliquity is m-
creased the value in low latitudes slowly diminishes, that in high
latitudes rapidly increases. The character of the resulting change
in distribution is first considered generally, and then with special
reference to the limits within which the obliquity is supposed to
vary, Stockwell’s limits 21° 58’ 36” and 24°36’ being used. Within
these limits the total range of Z, amounts at the equator to 93
per cent. of its present value, diminishes to zero in lat. 43° 20°; here
the sign of the change is reversed and the total range of L, in-
creases up to 104 per cent. at the pole. This alteration affects
both hemispheres alike.
For the normal annual amplitude ZL, the total range is in every
latitude 104 per cent. of its value, but this effect blends with
changes due to eccentricity, the influence of which appears on
transferring to mean time. This transformation is made for the
present position, numerical results being tabulated; and also for
those positions in which eccentricity has its most pronounced
influence in modifying the annual term, viz. when the line of
equinoxes is at right angles to the major axis of the orbit, making
the inequality in duration of summer and winter greatest.
If these epochs be described as genial and glacial, the first has
for element of heat-supply in north latitude expressed in mean
time
= Q’dt, where Q =L, —(L, — 2eL,) cos 27... ,
while for the second Q’=L,4+ (L, + 2eL,) cos 2at ... ;
only the more important terms of the coefficient of annual term
cos27t being here written. Attending only to these terms, in
high latitudes Z, is large, and a high value of eccentricity is
required to produce any considerable modification. But L,
vanishes on the equator and is small in low latitudes, while Z,
has its greatest value there, so that a moderate value of e makes
the difference between the two epochs quite considerable. One of
these formule is derivable from the other by changing the sign of
L, which is precisely the change made in passing from north to
south latitude.
Hence in so far as change of eccentricity is a vera causa for
glacial epochs it acts in opposite senses in the two hemispheres,
making a genial epoch in the one contemporaneous with a glacial
epoch in the other. Also apart from the minute effect mentioned
at the outset, the action of eccentricity is through the periodic
terms, whereas the alterations due to obliquity affect also the
non-periodic term. The effects of changes in obliquity of the
1896.] and tts dependence on Astronomical Elements. 71
ecliptic are small in low latitudes, and well marked in high
latitudes ; those of eccentricity, with appropriate position of peri-
helion, are conspicuous in low latitudes, while producing a fair
modification in high latitudes,
In each case the effects are so different in high and in low
latitudes that an average taken over so large a range as a hemi-
sphere quite obscures their special character.
The question of drawing inferences as to temperature is
rendered extremely complex by a variety of modifying conditions,
of which the principal is the action of the ocean and atmosphere
as carriers and reservoirs of heat. Apart from these, a solution for
temperature may be easily obtained, but it is important to observe
that it is necessary to take non-periodic and the various periodic
terms separately, these being affected with different multipliers
in the integration, and the latter subject each to a different
modification of phase. This may render the comparison of terms
such as midsummer and midwinter heat with the corresponding
temperatures seriously fallacious. It appears to be important in
every case to compare non-periodic only with non-periodic under
other conditions, amplitude of annual term with amplitude of
annual, and so on.
In order to estimate the effect of absorption, the transmitted
part is assumed to be equal to
@&+e,cos[+e,coPrl+...,
where J is angle between the rays and the normal to the surface.
This seems suited to express an absorption increasing as the
sun’s altitude diminishes, with considerable generality, and has
the advantage that each term is exactly integrable in the manner
of the diathermanous case.
This integration is effected, and some results tabulated, from
which it appears that in low latitudes the periodic terms are
exaggerated in comparison with non-periodic, the effect tailing
off as the pole is approached; the amount of the absorption being
of course much less for low than for high latitudes. This relative
alteration ought to be taken into account in drawing conclusions
as to temperature.
02 Dr Lazarus Barlow, On an Osmometer. [Feb. 10,
Monday, February 10, 1896.
PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR.
Professor H. Marshall Ward, Sc. D., Christ’s College, and W. H.
Duckworth, B.A., Fellow of Jesus College, were elected Fellows of
the Society.
The following communications were made:
(1) By Dr Lazarus Bartow.
The author exhibited an osmometer designed for the estimation
of the initial rate of osmosis and a modification of the same suitable
for the examination of small quantities of fluids. The principle
of both is the same, viz. that the stem of the osmometer is kept
horizontal, and the level of the fluid inside the osmometer is the
same as the level of the fluid outside the osmometer. The larger
instrument is fully described in the Journal of Physiology, vol. XIX.
1896, p. 140 and foll.; the smaller instrument differs from it in
that it is immersed in water until the stem of the osmometer
just shows above the surface. By these instruments the author
found that the initial rates of osmosis are not indicated by their
final osmotic pressures, or in other words by their freezing points ;
thus, to give an example, with a copper-ferrocyanide membrane
the initial rate of osmosis of a decinormal solution of urea was
half as great again as the rate of osmosis of a decinormal solu-
tion of glucose, whereas urea and glucose being indifferent sub-
stances, decinormal solutions of each have the same freezing point
and the same final osmotic pressure. The object for which the
research was performed was to see whether it is justifiable to apply
deductions from the freezing point of fluids existing in the animal
body to the question of lymph formation. Since the freezing point
determinations give no indications as to the relative amounts of
osmosis of two solutions of different composition at pressures
possible within the animal body, 2.e. approximately at atmospheric
pressure, application of the laws of osmosis which are true at final
osmotic pressures are not justifiable in the case of the animal body
where such pressures can at best but rarely occur.
1896.] Mr Bles, Nephrostomial Tubules. 73
(2) On the communication between peritoneal cavity and renal
veins through the nephrostomial tubules in the frog (R. temporaria).
By Epwarp J. BLEs, B.Sc.
The discovery of nephrostomes in the kidneys of adult Am-
phibia was announced by Spengel in his fine paper: Das Uro-
genitalsystem der Amphibien, published in 18761 In this he
showed clearly that the nephrostomial tubules in Urodeles and in
Ceecilia have a lumen persistent throughout life and always con-
tinuous with the perivisceral space at one end and with the
lumen of the neck of the Malpighian body at the other end.
Semper? and Balfour? had both described in 1874 a similar state of
things in the Wolffian bodies of Elasmobranch embryos, and
Semper‘ gave a list of Elasmobranchs in which the nephrostomes
remain open in the adult. Thus it was shown that in this respect
there is a close resemblance between adults of many species of
Elasmobranchs, Urodeles and Ceecilia.
When Spengel, however, examined the adult kidney of Anura,
although the nephrostomes were clearly visible, he could not trace
a single tubule from them into the neck of a Malpighian body.
F. Meyer of Leipzig, who discovered the “stomata,” as he called
them, independently of Spengel, was equally unable to find the
inner opening into a tubule of the kidney® The subject was next
investigated by M. Nussbaum who published in 1880 a short
paper’, without illustrations, containing the statement that the
nephrostomial tubules in adults of the genera Rana, Bufo and
Bombinator communicate at their inner ends with veins which he
identified with renal portal veins. This result was accepted by
Wiedersheim both in his Lehrbuch’ and his Grundriss* der ver-
gleichenden Anatomie der Wirbelthiere and in his portion of Ecker’s
Anatomie des Frosches*. Still the observations seem to have been
met with incredulity and Nussbaum with his pupil Wichmann
1 Arb. a. d. zool. zoot. Inst. d. Univ. Wiirzburg. Bd. ur. (1876), p.1. <A short
notice had already appeared early in 1875 in Centralbl. f. d. med. Wissensch.
No. 23.
2 «Ueber die Stammverwandtschaft der Wirbelthiere und Anneliden.” Centrbl.
f. d. med. Wiss. 1874. No..35.
3 @.J. M.S: 1874. Vol. x1v. N.S. p. 357.
4 «Seomentalorgane bei ausgewachsenen Haien.” Centrbl. f. d. med, Wiss.
1874. No. 52.
5 Fritz Meyer. “ Beitrag zur Anatomie des Urogenitalsystems der Selachier
und Amphibien.” Sitzber. d. Naturf. Ges. zu Leipzig. 1875. p. 38.
6 «*Ueber die Endigung der Wimpertrichter in der Niere der Anuren.” Zool.
Anz. 11. Jahrg. p. 514.
7 Qte Auflage. 1886. p. 758.
8 2te Auflage. 1888. p. 355. English ed. 1886. p. 307.
9 1882. p. 41.
74 Mr Bles, Nephrostomial Tubules. [Feb. 10,
paid further attention to the subject. Then, in 1886, they pub-
lished a paper? accompanied by drawings confirming, extending
and in one point correcting the earlier results. The figures show
that in Rana fusca, Rana esculenta, Bufo calamita and Alytes
obstetricans the nephrostomial tubules open into veins. Nussbaum
correctly identifies the veins as the roots of the vena cava posterior
and hence renal veins, not renal-portal. Figures are also given
showing how the nephrostomial tubules in young R. fusca larvee
open into the neck of the Malpighian body or into Bowman’s
capsule just as they do in adult Urodeles, and showing a stage
where the tubules end blindly after losing the above connection,
and finally a later stage with the venous communication. In spite
of this, C. K. Hoffmann in the same year? asserts that in adult
Rana, Bufo and Alytes the tubules in question end blindly, but
confirms the communication with the neck of the Malpighian body
in larve.
In the course of researches which were carried out by the late
Prof. A. M. Marshall and myself’, we were able to confirm
Nussbaum’s results and extend them to the English R. temporaria.
The adult kidney has a number of nephrostomial tubules which
appear to end blindly, but there are others which have distinct
inner openings into the renal veins.
In this form, generally considered as identical with R. fusca,
the development did not follow the same course. A rod of cells
given off from the segmental tubule in its early solid condition
grows towards the peritoneum, fuses with it and acquires a lumen
from the peritoneum inwards. Before the lumen has reached the
inner end of the tubule this end loses its connection with the
segmental tubule and the nephrostomial tubule ends blindly. This
occurs in tadpoles 17—18 mm. long, but in 21 mm. tadpoles the
tubule has acquired its connection with the renal vein.
The course of development is evidently coenogenetic in this
species as compared with &. fusca, as it is in other respects in
comparison with £. esculenta. This divergence, therefore, cannot
invalidate Nussbaum’s results and Hoffmann’s confirmation of
them, and Prof. Marshall did not hesitate to incorporate the main
facts into his Vertebrate E’mbryology (p. 192).
Nevertheless there are still many who refuse to acknowledge
the existence of so direct a communication between body-cavity
and the circulatory system, and for that reason I considered
1 “Zur Kenntniss der Nierenorgane.” Arch. f. mikr. Anat.xxvil. 1886. pp.466-
9 and plate 23.
2 “Zur Entwicklungsgeschichte der Urogenitalorgane bei den Anamnia.” Z.W.Z.
Vol. xutv. p. 594.
> The development of the kidneys and fat-bodies in the Frog. Studies Biol. Lab.
Owens Coll. Vol. 11. 1890. p. 183.
1896.] Mr Bles, Nephrostomial Tubules. 75
it worth while to exhibit before this Society specimens to demon-
strate the point.
A kidney of a common frog (not one year old) was hardened in
Hermann’s fluid, imbedded in paraffin after gradual impregnation
in xylol and paraffin, cut in a series of sections and stained on the
slides either with aniline blue-black or by the Biondi-Heidenhain
(acid) method. The latter gives plasma well stained with fuchsin
and blood corpuscles differentiated with methyl green. A bunch
of flagella can be seen protruding through the imner opening of
the tubule into a space lined with squamous endothelial cells, and
either containing blood corpuscles or standing in open communi-
cation with similar spaces on the adjoining sections which do
contain blood corpuscles. These vascular spaces can easily be
traced into the renal veins. On all four sections shown the peri-
toneal opening of the tubule could also be seen. On one section
a nephrostomial tubule could be traced from the peritoneum and
running towards the flagellate neck of a Malpighian body, but
just short of reaching this opening into a narrow space lined
with endothelium and containing a blood corpuscle, the space
being continuous with venous spaces on neighbouring sections.
These facts do not stand alone as isolated instances of a
channel of communication between ccelom and vascular system.
Mr Shipley read a paper before this Society in 1888 (Proc. Phil.
Soc. vol. vi. p. 218) in which he cites, with the exception of
M. Nussbaum’s, the cases occurring in the animal kingdom of
such a communication.
Some of these cases still hold good and amongst them cer-
tainly the communication through the peritoneal stomata of the
diaphragm in mammals from the great abdominal serous cavity
through the lymphatic spaces and ducts into the great veins.
Physiologically these lymph channels can be compared with
what exists in the above-mentioned five forms of Anura. The
perivisceral cavity is a lymph space continuous with the cisterna |
magna lymphatica and passing lymph into it, and there are reasons
for thinking that the peritoneal lymph can also pass into the renal
veins through the nephrostomes.
Anatomically considered, the adult Rana fusca can be easily
brought into line with the other Amphibia with respect to its
nephrostomial tubules when it is borne in mind that the larva in
its ontogeny passes through stages in which the tubules have
successively relations corresponding (1) to the tubules in adult
Urodela, (2) to an indifferent condition still persisting in part in
other adult Anura, viz. ending blindly, (3) to a condition which
occurs in at least four other forms of Anura and easily derived
from the indifferent condition.
76 Mr Darwin and Miss Pertz, On the effect of [Feb. 10,
(3) On the effect of water currents on the assimilation of
aquatic plants. By Francis Darwin, M.A., F.R.S., and D. F. M.
PERTZ.
The principal fact established by our research is the notable
increase in the gas given off by certain aquatic plants in the
process of assimilation, when the water in which they are culti-
vated is disturbed by stirring.
The fact is of interest as bearing on our general knowledge of
the gaseous interchange in aquatic plants. It also bears on the
nutrition of these plants in still and running water. Moreover it
is of interest on the question of method, 2.e. on the question of
how far the yield of gas represents assimilative activity.
This last point is illustrated by the history of our research
which began with a chance observation made a few years ago.
If a small quantity (about 5 p.c.) of alcohol is added to the
water in which a sprig of Hlodea canadensis is bubbling under
the influence of light, the rate of bubbling at once shows a con-
siderable temporary increase. It becomes about twice as quick,
and returns to its normal pace in four or five minutes.
It seemed possible that the plant was stimulated by the alcohol,
but it appeared more probable that the result was physical rather
than physiological. We therefore fitted up a simple apparatus
by means of which air was forced by the pressure of a column
of water to escape through a capillary tube (0:2 to 03 mm.)
into a beaker of water. The air ceased to escape from the tube
while the column of water showed a pressure of about 20 cm.
When alcohol was added in such a way as to mix with the water in
the beaker close to the opening of the tube, air at once escaped
from the capillary and the water column fell several cm. This
result obviously depends on the fact that the surface-tension of
a mixture of alcohol and water is less than that of water.
To discover whether the effect of alcohol on water-plants
also depended on diminished surface-tension at the pomt of
escape of the bubbles, it was necessary to eliminate the possible
stimulative effect of alcohol on the leaves. This was done by
Devaux’s method’. The tube of a funnel was cut short below the
conical part, and in this opening the stalk of a Hottonia was held
by a plug of cotton-wool, so that the cut end projected mto the
expanded part of the funnel. Melted gelatine was then poured in
from above, which became solid rapidly and thus closed the funnel
below with a water-tight plug through which the stalk passed.
The main body of the plant could now be immersed in a beaker
of water, while the bubbles from the cut end of the stalk escaped
into water contained in the funnel. When alcohol (5 p.c.) was
1 Annales des Sciences Naturelles, 1x. 1889. p. 67. In our experiments the
plant is in a reversed position to that figured by Devaux.
1896.] water currents on the assimilation of aquatic plants. Cie
added to the water in the funnel the rate of bubbling became
about eight times as quick, returning after two minutes to about
its previous rate.
p-m. Rate
2.21 14
2.23 14 5 pc. spirit added
2.25 111
2.27 18
A similar striking effect was obtained by adding 10 p.c. after a
few minutes. Later in the day the effect was not so marked,
the rate of bubbling was doubled when alcohol was added to the
water in the funnel. The result is what might have been ex-
pected since the escape of gas varies with the pressure at the
cut end of the stalk. This well-known fact may be simply demon-
strated by cementing the cut stalk with gelatine into the lower
end of a vertical tube which is filled with water to various heights
by means of a side opening and rubber tube, and thus exposes the
cut end of the stalk to varying pressures.
The following table shows a diminution in, and final cessation
of, the bubbling as the pressure rises, and a rise as it is allowed to
fall again.
27th June, 1895. LHlodea canadensis.
Time Pressure Rate Temperature
ce | 15 em. 66
me \ 24 cm. Al 21-40
- } 30 cm. 50 91-4
x 51 em. 33 21°4
a } 64 cm. 14 21-4
ee | 80 cm. 0 91:3
Ba 64 em. 15 21.3
fe 51 cm. 30
a } 30 cm. 71 21:2
s k 15 cm. 166 21-2
78 Mr Darwin and Miss Pertz, On the effect of [¥Feb. 10,
Having shown that alcohol added to the water in the funnel
increases the rate of bubbling by diminishing the surface-tension,
we expected to find that alcohol, added to the beaker in which the
leaves were, would produce either no effect or less than the normal
effect. It turned out however that the addition of alcohol to
the beaker produced nearly the usual effect. This proved that the
accelerating effect produced by alcohol when the cut stalk and
the leaves are in the same vessel of water is not simply due to
diminished surface-tension, although this cause undoubtedly has
some effect.
At this pomt Mr Blackman made the useful suggestion that
water should be added instead of alcohol. It was found that
this treatment greatly increased the rate of bubbling, and it
at once became clear that this result and the chief part of the
alcohol effect were due to the currents set up in the water by
the act of pouring in the fluid, water or alcohol as the case may
be. This was confirmed by gently stirring the surface-water with
a rod, until, by the movement of small particles floatmg im the
water, it could be seen that the lower strata were in rotation.
Under this treatment the rate of bubbling at once became
nearly doubled. It should be noted that the plant was not visibly
shaken or moved, so that the effect was not due to the bubbles
being helped to escape by mechanical shock. This point is worth
mention, because a blow on the table was found to cause a slight
escape of gas from the glass capillary of the above described
apparatus at a pressure which had ceased to produce a flow of
bubbles.
Method.
-The experiments were made in a dark room illuminated by
one of the Incandescent Gas Company’s burners, in which a
white-hot mantle, surrounding an argand flame, gives a brilliant
steady light. Between the gas and the vessel in which was the
bubbling plant we placed a glass trough through which a current
of water flowed. In this way the plants could be kept at a tempe-
rature sufficiently constant.
The plant to be experimented on was tied to a glass rod sup-
ported vertically in a beaker of water. In all the earlier ex-
periments the yield of gas was estimated by taking with a
stop-watch the time which elapses during the evolution of a given
number of bubbles. The reciprocals of these times will be pro-
portional to the rate of bubbling. The “rates” given in our
experiments are simply derived from the reciprocals by moving
the decimal place. The “rates” are comparable throughout any
given experiment, but the rate in one experiment is not neces-
sarily comparable with that in any other.
1896.] water currents on the assimilation of aquatic plants. 79
In our later experiments the gas yielded during half-an-hour
was collected and measured in the modification of Timiriazeff’s
Eudiometer described and figured in Darwin and Acton’s Prac-
tical Physiology}.
As the times involved were short, and the temperature re-
mained fairly steady during the experiments, we dispensed with
barometric and thermometric corrections, and we believe that
the readings of the eudiometer are fairly comparable inter se
during any given experiment: although they certainly do not
give absolute amounts with accuracy. It will be seen that the
variations in the yield of gas as given by the eudiometer do
not always agree with the rates obtained by timing the bubbles
given off. When this is the case, we are inclined to trust the
eudiometer readings rather than those of the stop-watch.
To stir the water uniformly, we hung a microscopic slide
to an ordinary bottle-jack, such as is used for roasting meat. The
glass slide makes five turns in about four seconds, and then reverses
and rotates in the opposite direction.
Experiments with Elodea.
In the following experiments we have given the average
rate of bubbling during periods in which the water was alter-
nately left quiet and disturbed. Where the amount of gas
yielded during the same period was measured the rate of yield
per minute is given in terms of a graduation of the eudiometer :
each graduation is equal to 0:01 c.c., and is of such a length that
the quantity of gas can be roughly read to 0:002 c.c.
A single experiment is given in full, in order that it may be
seen that the effect of stirring is fairly well kept up for a period of
half-an-hour.
1 Edition 1. p. 45.
80 Mr Darwin and Miss Pertz, On the effect of [Feb. 10,
Experiment 1: 5th June, 1895. Llodea.
a.m. Rate! Temp.
10.37 100 15-4
100
47 76
47-5 76
56 62 Still
11 66
if 5D
8 76
74
10 62 15-4
12 Started jack
12°5 166
166
200
13 200 15-7
200
14 200
15 200
16 166
18 166
166 Stirred
20 166
21 142
23 142
25:5 166
27 166
29 153
30 41) | (Sudden change in rate of
32 a bubbling for 3 minutes.)
33 125
43
35°5 181
181 Stopped jack 16
37 153 Gp
38 111 |
40 90
|} 43 83
46 86 S45
50 80 Still
53 76
76
55 76
12.3 tel 16-4
1 rate means rate of bubbling calculated from the readings of the stop watch.
1896.] water currents on the assimilation of aquatic plants.
p.m. Rate
yt
125
142
142
5 166
166
142
6 142
9 166
153
ll 153
15 142
15°5 153"
16 142
18 142
142
19 133
Dil 1325
23 125
ee vy elas
26 100
27 100
29 100
30 105
IEF
30 105
Temp.
Started jack 166
Stirred
16°8
WOT Ex. Pl. iT:
81
82 Mr Darwin and Miss Pertz, On the effect of [Feb. 10,
Experiment 2: Ist June, 1895.
Elodea in Tap-water.
a.m. Time Rate Temp.
Hoey 16m. | Still 45 19-4C.
9 7
ae 25 m. Stirred 7A = :
11.57 20
ion Vim | SH 27 ae
., isan, | SHimed | oy 20-2
Experiment 3: 4th June, 1895.
Elodea in Tap-water.
a.m. | Time | | os | be
uy re 40 m. Still 40 i
Ts, 26 m. Stirred 50 167
i Oa. Stirred 30 a
A 20m. | Still | 13 | 17-2
C nat 12m Stirred 29 | i
1896.] water currents on the assimilation of aquatic plants. 83
Experiment 4: 5th June, 1895.
Elodea in Tap-water.
a.m. Time | | Rate | Temp.
10.37 ;
eis \ 33m. | Still | 76 | 15-4C.
ise } 17m. | Stirred | 166 | 15-4
a ies } | Pe | . | 40 | 158
11.33
9 35-5} seas és | ee | po
as } | 26 m | Still 90 16-2
12.4 16-6
, BT } 33m. Stirred 142 16:8
12.38
, BB | 17m Me 34 17
t | |
cele | ean | Still | 29 | 17-1
Experiment 5: 6th June, 1895.
Elodea in Tap-water.
| Time | Rate | Temp.
9.33 13-6 C
103} 53m. | Still | 76 We
10.29 14:5
ish | 44m Stirred 111 14:8
84 Mr Darwin and Miss Pertz, On the effect of [Feb. 10,
Experiment 6: 10th October, 1895.
Elodea. Fresh Tap-water.
a.m. | Time Rate Quantity ? Temp.
10.35 .
nie \ 30 m. Still 18 13 18 C.
eth Aan | eee | Ae 27 18
a0 30 m. | Still | 15 Ag 18
Experiment 7: 12th October, 1895.
Elodea, Fresh Tap-water.
a.m. | Time | Rate Quantity | Temp.
Sil Slim: Still 14 17 18 C.
Soe Anam | Siteeal | - a0 35 18
tea Bllim, || Seni 6 25 18
1 rate means rate of bubbling.
2 quantity means amount of gas collected, expressed in eudiometer-graduations
per minute,
1896.] water currents on the assimilation of aquatic plants. 85
Experiment 8: 21st November, 1895.
Elodea. Old Tap-water.
Aan Time | | Eafe’ | Oaaray |e Temp:
niet 35m. | Still 52 10 15C.
mcr Bin, 1) Seiecedhl| 9 45 ‘Id | 185
1236 30m, Stil 30 | 08 16
aait 30 m. | Strredsl)) 28 | AI
Experiment 9: 9th October, 1895.
Elodea in Fresh Tap-water.
unde Rate | Quantity | Temp.
16m., 4 »,Still 19 31 16-5 0.
15m. Stirred 25 D8 16:5
teams Pe Sei 12 - 36 16-5
15 m. Stirred a ‘48
15m. | Still 45 31 | 165
Lam: Stirred | 22 | Z510) 16°5
86 Mr Darwin and Miss Pertz, On the effect of (Feb. 10,
Experiment 10: 20th November, 1895.
Elodea in Tap-water which had stood 24 hours.
a.m, Time Rate Quantity Temp.
10.23 ;
i115 BOn ese 16 08 150.
| NOsrwerl) Kittel | 9% 10 fs
= apf 39 m. Still 17 06 16
ei Wem | Sheed | 22 12 16°5
Altogether eleven experiments were made with Elodea.
The results are fairly uniform, that is to say, the rate of bubbling
- as taken by the stop-watch is nearly always markedly increased.
Exceptions occur, however: for instance, in the “stirred” periods
of Experiment 8 stirring did not increase the rate of bubbling,
but in both cases the amount of gas actually yielded was greater.
The same thing is true of the final “stirred” period of Experi-
ment 9. Indeed there were no exceptions to the statement that
the actual yield of gas per minute was greater when the water was
stirred. We are inclined to believe that the results obtamed by
measuring the gas are trustworthy because the amount of effect
due to change of condition does not vary greatly. The following
figures give, in round numbers, the effect of change from the
“stirred” to the “ still” condition.
180 : 100
1
75: ery
16k fi
ea wee
M65. 1,
1896.] water currents on the assimilation of aquatic plants. 87
Experiments with Hottonia palustris.
Only two experiments were made with this species: the results
agree with those obtained for EHlodea.
Experiment 11: 10th June, 1895.
Hottonia.
a.m. Time Rate Temp.
he 35m. | Still 43 165 C
” 35 ; ;
et Sse Saaremaa He ;
teh | 4m. | Still 37
Experiment 12: 15th August, 1895.
Hottonia. Old Tap-water.
|
p.m. |; Pime Rate Quantity Temp.
12 : ;
29 29 m. Still 21 22 24C
12.3) | aim. | Stirred | 35 32
Experiments with Potamogeton bilupsii.
This plant, which is said to be a cross between P. coriaceus and
P. plantagineus, happened to occur in convenient quantities in the
Botanic Garden and was therefore used.
The results were of a conflicting character: in two experiments
in which freshly-drawn tap-water was used, the stirring un-
doubtedly produced an increase in the yield of gas. But in the
other ten experiments for which water was used which had stood
in an open vessel for twenty-four hours, the stirring produced
either increase or decrease or else was without effect on the yield
of gas.
88 Mr Darwin and Miss Pertz, On the effect of [Feb. 10,
Cause of the phenomenon in Elodea.
There can be no doubt that the increased yield of gas when
the water is stirred is simply due to the movement of the water
bringing the leaves rapidly in contact with fresh layers of water
and thus hastening the process of diffusion. It illustrates in fact
the same phenomenon as the well-known experiment in which a
strong solution of a coloured salt (e.g. potassium bichromate) is
covered by a layer of water in order to demonstrate the extreme
slowness with which the yellow colour spreads to the upper layers
if the jar is undisturbed.
It is clear that the effect of stirrmg on water-plants is a
physical phenomenon in the sense that it is not necessarily con-
nected with the act of assimilation.
This is proved by taking advantage of the fact that aquatic
plants placed in water highly charged with gas give off bubbles in
the dark}.
We observed this form of bubbling by using a feeble illu-
mination just enough to enable us to count the bubbles, but quite
insufficient for assimilation. When the water was stirred the rate
of bubbling was clearly increased. In other cases where the dark-
bubbling had ceased, 1t was started again by means of stirring.
Assimilation.
The question whether the increase in the yield of free gas
produced by stirring necessarily implies increased assimilation
is one to which we cannot give a complete answer.
The solution involves a more complete control of the physical
conditions than obtained in our experiments, as well as analytical
data which we cannot at present supply.
The gaseous exchange of an aquatic plant does not necessarily
involve any yield of free gas, it depends primarily on diffusion
of dissolved gases both into and out of the plant. The escape
of bubbles is, as Devaux and others have pointed out, an accidental
occurrence depending on the existence of fortuitous openings into
the intercellular spaces. It is clear therefore that the yield of
free gas cannot, without further inquiry, be assumed to represent
assimilation.
There is, moreover, as already pointed out, an evolution of
gas quite independent of the action of light, depending on the gas-
pressure in the water. Devaux has explained how it is that, in
spite of the above considerations, the rate at which gas is
given off does fairly well represent the activity of assimilation.
1 See Devaux, dnnales des Sc. Nat., 1889, p. 38, where the literature of the
subject is given.
1896.] water currents on the assimilation of aquatic plants. 89
The oxygen which arises as a bye-product of assimilation is less
diffusible than the CO, absorbed, and this necessarily leads to a
rise of gas-pressure in the intercellular spaces, and to an escape of
the internal atmosphere at any openings which may exist. It
therefore follows that the more vigorous the assimilation becomes
the more rapid is the escape.
We have shown that in some cases at least stirring the water
produces an increased yield of gas, there is therefore prima facie
evidence that assimilation is actually increased. But unless we
can ascertain in what way the amount of oxygen yielded as free
gas and by diffusion is affected by stirring, we cannot be sure
of the point.
We have made a few analyses of the gas collected over water
from Hlodea, using water which had stood for twenty-four hours as
well as freshly-drawn water, so as to avoid errors from bubbling
due to gas-pressure.
Elodea. Feb. 13, 1896. Fresh Tap-water.
O per cent.
9.58 to 11.34 am. | still 22
11.38 a.m. to 12.43 p.m. | stirred | 20
Feb. 17, 1896. Fresh Tap-water.
9.55 to 11.10 a.m. stirred | 19
11.13 a.m. to 1.10 p.m. | still 22
Feb. 12, 1896. Old Tap-water.
9.55 to 11.32ta.m..|) still 22
11.38 a.m. to 12.44 p.m. | stirred | 19
Feb. 18, 1896.
10 to 11.23 a.m. | stirred | 19
11.26 a.m. to 12.45 p.m. | _ still 20
The percentage of oxygen is remarkably low in these cases.
Devaux found the percentage of oxygen yielded by Hlodea in
the light to be about 25 p.c., and we have, in earlier experiments,
found a similar proportion. On the other hand we have also
found Elodea yielding no more than 20 p.c. when the evolution
of gas was certainly nearly all due to assimilation since it was
diminished to a quarter of its former amount by darkening the
plant.
Moreover, Devaux has shown that in darkness Hlodea may
give off gas containing only 16 p.c. of oxygen, and we have found
that Hottonia may only give off 14 p.c. of oxygen. It seems
possible therefore that a yield of 19 p.c. of oxygen may be an
index of assimilative activity.
90 Mr Burkill, On a collection of Plants [Feb. 10,
With Hottonia the few experiments we made were more satis-
factory.
Aug. 1. Old Tap-water.
still 23 p.c. oxygen
stirred 22 ,, si
Aug. 2. Old Tap-water.
still 9923
stirred 23
In the case of Potamogeton the results were conflicting, but on
striking an average it was clear that no marked effect on the
percentage of oxygen was produced by stirring.
It is worth noting that the percentage of oxygen yielded by
Potamogeton is always much higher than that given by Hlodea or
Hottonia, being occasionally as high as 58 per cent. We are
unable to suggest a reason for this difference. For Elodea and
Hottonia the case stands thus: stirrmg does not seem markedly
to affect the percentage of oxygen, while it increases the yield of
gas. If so, the total amount of free oxygen yielded must be
increased, and this probably implies increased assimilation.
Although the evidence from gas analysis is not conclusive, we
have shown by a direct evidence that assimilation is increased by
movement of the water.
This was proved to be the case by cultivating water-plants
in still and running water, and observing, by means of Sachs’
iodine-test, the relative amounts of starch produced. The plants
were de-starched by darkness before being used for the experi-
ment, and care was taken to ensure identity of temperature and
illumination. Two trials were made with Hlodea and one with
Potamogeton, with identical results; namely, that all the specimens
from the running water contained distinctly more starch than those
from the still water. :
(4) On a collection of plants from New Britain (New Pommern).
By I. H. BurkI1u, M.A., Gonville and Caius College.
In 1875 Baron A. von Hiigel visited several islands in the
Pacific, and brought back collections of plants from Ovalau in the
Fiji group, Upolu in the Samoa group, from the Duke of York’s
Island (New Lauenburg), and from New Britain. The last-named
island he was unable to visit in person, and had, therefore, to
entrust the collecting entirely to his collector. Unfortunately a
number of accidents caused the loss of a large part of the
collections, and the remaining material only represents a portion
of what had been obtained. These collections were subsequently
presented to the University Herbarium.
1896.] from New Britain (New Pommern). 91
The specimens from Ovalau proved to be all known Fijian
forms ; so also those from Upolu were, with one exception—a new
orchid!,—known Samoan forms. Our knowledge of the botany of
New Britain is very incomplete, and consequently the following
enumeration will be found to contain the names of many plants
hitherto unknown from this island. At the end of this paper
is a bibliographical list to which reference will be made by
means of roman numerals.
One early botanist, Commergon, who accompanied Bougainville
in his voyage round the world, came very near to landing on New
Britain; but the island, called New Britain in the narrative of the
voyage, is in reality New Ireland. The part of New Ireland visited
by him is in the south, or New Britain end of the island—a district,
Bougainville says, ‘not very rich for the botanist’. Commergon’s
collections, including more than 3000 species from all parts of the
world, which he never lived to bring to Europe, lie in the Paris
Museum ; but it must be remembered that it is erroneous to refer
to any of them as from New Britain.
The north end of New Britain, constituting the Gazelle Penin-
sula, though not yet completely explored, is known to be a very
rugged region with steep volcanic mountains, rising to considerable
heights in Mts Fitzgerald and Beautemps Beaupré. On the north
coast of this peninsula les Blanche Bay, in the neighbourhood of
which these plants were collected. The bay les under a range of
hills rising to 2000 feet and containing an active volcano. Our
knowledge of the botany of the island is practically confined to
its vicinity. The interior, as indeed the greater part of the coast,
remains a terra incognita.
New Britain is by no means isolated. The channel between it
and New Ireland (New Mecklenburg) is only 30 miles wide, and
in it lies the Duke of York’s Island (New Lauenburg) with its
attendant islets: through this long island of New Ireland we have
a land-link to the island of New Hannover, and so to the Admiralty
Isles. To the South-east at no very great distance le the
Solomon Isles; but unfortunately the island of Bougainville,
which is the nearest, is the least known. The western extremity
of New Britain approaches very near the coast of New Guinea,
and the gap between the two islands is bridged over by a number
of islets. From its geographical position, we should then expect
New Britain to possess a flora of a Papuan type, and such indeed
the fauna seems to be’*.
1 Rolfe, New Orchids. Decade 17. Kew Bulletin of Miscellaneous Information,
96.
2 A Voyage round the World. English edit., London, 1772, p. 330.
3 Wallace, Australasia. London, 1888, p. 469.
92 Mr Burkill, On a collection of Plants [Feb. 10,
ENUMERATION OF SPECIES
obtained in the vicinity of Blanche Bay.
PTERIDOPHYTA.
Asplenium Nidus L.
Aspleniwm falcatum L.
Nephrodium latifolium Baker.
Nephrolepis acuta Presl.
Polypodium adnascens Sw.
Polypodiwm sinuosum Wall.
Polypodium [inne Bory.
Lycopodium carinatum Desv.
Selaginella canaliculata Baker.
ANGIOSPERMH.
Monocotyledones.
Panicum jgavanicum Poiret.
Centotheca lappacea Desv. (recorded XVIIL).
Mariscus Sieberianus Nees.
Calamus sp.
Cordyline terminalis Kth. var 71 Baker.
Alpinia (Hellenia) oceanica mihi (A. nutans K. Schum.
non Rose.) (recorded xvi.). Professor Schumann has described
this species, although not yet found in New Guinea, in the
flora of Kaiser Wilhelms Land?, and, supposing it to be a
form described by Rumphius, on which Linnezus founded his
species Globba nutans, named it Alpima nutans. I cannot agree
with him in this complicating of the synonymy. The matter
may be sifted somewhat as follows. In the Herbariwm Ambot-
nense? Rumphius describes five species of Globba, of which the last
Globba sylvestris was found in two forms; these he distinguishes as
Globba sylvestris major and Globba sylvestris minor sive florida’.
Linneus did not see even varietal ditference between them, and
called Globba sylvestris of Rumphius Globba nutans’. Subsequently
Roscoe® thought his Alpinia nutans to be Globba nutans L., the
two being in size and habit somewhat similar, but probably erred.
Miquel® saw in Alpinia gigantea Bl. one element of Linnzeus’ species,
1 Schumann u. Hollrung, Flora von Kaiser Wilhelms Land. Berlin 1889,
28
p. 28.
2 Amsterdam 1750. Lib. x1. Cap. xx1x.
3 loc. cit. Cap. XXXII.
4 Mantissa, ii. Stockholm 1767, p. 170.
5 Roscoe in Smith, Ezotic Botany, 1. London 1805, p. 93, and Monandrian
plants of the order Scitamineae. Liverpool, 1828, t. 73.
6 Flora Indiae batavae, 11. Amsterdam 1855, p. 605.
1896.] from New Britain (Neu Pommern). 93
namely Rumphius’ form major; and there are many reasons which
make one regard this as correct. Now Schumann sees in his
Alpinia nutans the other element, namely Globba sylvestris minor,
—a decision the correctness of which is questionable. The follow-
ing statements give the reasons for and against Schumann’s iden-
tification.
Alpinia nutans K. Schum. agrees with Globba sylvestris minor
in its nodding inflorescence, persistent bracts, leaves less than two
palms’ breadths broad, and narrow petals. In other points, however,
it differs, thus :—leaves oblanceolate instead of lanceolate and not
undulate (cf. Rumphius’ figure LXIII.), tapering very rapidly above
to a shortly acuminate point, flower not conspicuously red, yellow
and white. The reader, remembering the difficulties which beset
the identification of species of Alpinia, will form his own opinion
upon the necessity of caution in this case. The probabilities seem
to be in favour of the following decisions being correct.
Alpinia nutans Roscoe (1805), not known till described by
Wendland! as Zerumbet speciosum in 1798.
Alpinia gigantea Blume (1830), apparently the plant figured
by Rumphius as Globba sylvestris major, and therefore is Globba
nutans L.
Alpinia nutans K. Schumann (1889) may possibly be, but
probably is not, Globba sylvestris minor, but if so is also Globba
nutans L. For this last species I propose the name A. oceantca.
Hollrung collected A. oceanica on the two islets of Mioko and
Kerawara belonging to the New Lauenburg group’; Warburg has
obtained it from Kerawara and the north of New Britain (XVII).
In the Kew Herbarium are specimens from the following sources:
Quadalcanar, Solomon Isles, Milne, 1855,—Admiralty Isles, Moseley,
‘Challenger’ Expedition,—and New Ireland, Barclay*. All these
localities lie fairly close together, the most westerly being more
than 1200 miles from Amboyna.
A. oceanica lies very near A. scabra Benth. from British India,
and is easily distinguished from other species of the section Hellenia
with a nodding inflorescence such as A. decurva Ridley.
Baron von Hiigel’s specimens lead one to suppose that the
curvature of the inflorescence becomes more marked as it grows
older, being very slight when the buds first begin to open, In
cases where the flowers are much crowded the axis of the inflor-
escence becomes twisted so as to obscure the 4 divergence which
is present. Such might account for the want of it in Rumphius’
figure.
1 Schrader et Wendland, Sertum Hannoverianum, tv. Gottingen, 1798, 3, t. 19.
2 Flora v. Kaiser Wilhelms Land. loc. cit.
3 Bentham recognised it as a new species. Enumeration of plants collected in
the Feejee Islands, Tanna, New Ireland and New Guinea. Hooker’s Lond. Journ.
of Bot. 11. (1843), p. 235,
94, Mr Burkill, On a collection of Plants [Feb. 10,
Dicotyledones.
Piper caninum Dietz.
Pouzolzia indica Gaudich. (recorded XVIII).
Ficus tinctoria Forst.
Amarantus melancholicus L. var. tricolor Lam. (recorded from
Blanche Bay 111.), and also an intermediate form approaching the
type.
Celosia cristata L.
Muehlenbeckia platyclados Meissn. (recorded VIII).
Clematis aristata R. Br. var Pickering O. Kze.
Indigofera Anil L.
Desmodium wmbellatum D.C. (recorded XvIt1.).
Uraria lagopoides D.C.
Phaseolus Mungo UL. (recorded 1x. and Xv.).
Vigna retusa Walp. (recorded XVIII).
Cassia glauca Lam.
Soulamea amara L. (recorded vViil.).
Mallotus ricinoides Mill. Arg.
Macaranga sp. near WM. tanarius Mill. Ar ge. ff only. | The
pith has been bored, probably by an ant; the leaves, which are
very similar to those of I. tanarius, bear on the upper surface near
the base 5—7 nectaries. Doubtless it is myrmecophilous. |
Cordieum variegatum Bl. both the variegated form and that
with green leaves.
Phyllanthus Finschti K. Schum. (recorded xvut). To the
known distribution of this plant,—viz. New Guinea (XvV.) up to
1800 metres!, Gazelle peninsula and Mioko (xvut.),—I can add
New Ireland, from whence a specimen collected by Barclay is pre-
served in the Kew Herbarium. The proportion of ¥ flowers to
¢ must be very high if the trees are equally divided between the
two sexes.
Schmidelia littoralis Bl.
Colubrina asiatica Brongn.
Calophyllum imophyltlum L.
Triumfetta suffruticosa Bl. (2)
Thespesia populnea Soland.
Abutilon graveolens W. and A.
Urena lobata L. (recorded vu.) var. scabriuscula Mast.
Hibiscus rosa-sinensis L. flore pleno.
Hibiscus tiliaceus L.
Sida rhombifolia L.
Melochia indica Wall.
Dischidia Collyris Wall. (recorded XV1I1.).
u Warbares Bergpflanzen aus Kaiser Wilhelms Land. Engler’s Bot. Jahrb.
xvi, (1893), p. 14.
1896.] from New Britain (Neu Pommern). 95
L[pomea Turpethum R. Br.
Physalis minima Don. (recorded 111.).
Solanum tetrandum R. Br.
Hemigraphis reptans Eng).
Eranthemum Huegelii mihi n. sp. Caulis fulvide scaber.
Folia lanceolata, in petiolos sensim contracta, supra minute sca-
brida, subtus nervis exceptis glabra, nervis lateralibus utrinque
10—12 arcuatim ascendentibus. Inflorescentia foliis longior,
floribus in cymulis, infimis 2—3-floris, supernis 1-floris, dispositis,
pedicellis quam bracteis subulatis longioribus, calyci eequilongis.
Calyx, apicibus glabrescentibus exceptis, glaber, laciniis anguste
linearilanceolatis quam tubo 3—4-plo longioribus. Corolle tubus
longus, lobis oblongis 3—4-plo longior. Antherz ultra fauces
exserte.
The leaves have the lamina about 15 cm. in length by 4 cm.
in breadth, and resemble considerably those of Hranthemum malac-
cense Clarke; the petiole is less than 2 cm. long: the flower is
most conspicuous, having a tube 3°5 to 4 cm. long and lobes up-
wards of 15 mm. long: the ovary is about 2 cm. long when ripe,
and carries 4 seeds: the anthers are exserted to the distance of
3 mm.
Of two inflorescences, in one the lower part carries no deve-
loped flowers, and in the other the lowermost flowers appear to
be cleistogamic, while the upper ones are chasmogamic. Cleisto-
gamy is known in the Indian members of the genus from the re-
searches of Kurz? and Scott”.
E. affine Warbg. (Xvul.) connects #. Huegelii with EF. paci-
ficwm Engl. (111.), but is quite distinct. H. Huegelit is a more
robust plant than H. malaccense. E. affine and E. pacificum are
known from the neighbourhood of New Britain, and £. malaccense
only from the Western Malayan region. LH. Huegeli belongs, like
all these species here mentioned, to Lindau’s genus Pseuderan-
themum’.
Eranthemum sp. near E. laxiflorum A. Gray.
Tournefortia argentea Forst.
Leucas flaccida R. Br.
Orthosiphon stamineus Benth.
Callicarpa pedunculata R. Br.
Callicarpa eriochlona Schauer. This plant, first described
from the Philippine Isles and since found in New Guinea, is by
no means identical with C. cana L. to which it has been united.
1 Dimorphism in Eranthemum. Journ. of Bot. x. (1872), p. 46.
2 Dimorphism in Eranthemum. Journ, of Bot. x. (1872), p. 161.
3 Xantheranthemum und Pseuderanthemum, zwei neue Gattungsnamen d. Acan-
thaceen. Gartenflora, 1893, p. 612.
96 Mr Burkill, On a collection of Plants [Feb. 10,
C. cana has a hoary appearance due to stellate hairs which branch
once or rarely a second time; while C. eriochlona is very densely
covered on the stems and below the leaves with a dense wool
of tawny shaggy hairs branching 4—8 times or even more.
Morinda citrifolia L.
Benincasa cerifera Savi.
Scevola Kenigit Vahl.
Wedelia strigulosa D.C.
In concluding it may be well to gather together the shreds of
information which we possess on New Britain botany, and see
what can be constructed out of them. In the various papers
hitherto published we find mention of just over 160 species,—a
fact which testifies to our ignorance of its flora. Of these species
a considerable portion consists of wide-spread plants common on
the Pacific and Malayan coasts, and some such as Touwrnefortia
argentea and Bea Commersoni R. Br.* which are confined to a
coral formation. About two-thirds of the whole number are
known from German New Guinea, one-seventh from the little-
known Admiralty Isles, a fair percentage from the Solomon Isles,
and barely one-half from Fiji. A small number of new species,
described from specimens from New Britain, have not yet been
discovered elsewhere; but it is very improbable that most of these
are endemic forms.
An island which helps to connect three regions such as
Australia, Malaya and Polynesia, may be expected to yield in-
teresting results in botanical geography; but at present many
years must pass before this is brought about.
A few of the specimens in Baron v. Hiigel’s collection could
not be determined: among them were three species of Ficus which
were too imperfect, a Macaranga (?) probably new, and some others.
Finally, I wish to tender my sincere thanks to the members of the
staff of the Kew Herbarium, to Mr C. B. Clarke and to Baron Sir
Ferdinand von Mueller for the considerable assistance which they
have given me, and most especially to Baron A. von Hiigel for the
many kindnesses which I have received from him.
BIBLIOGRAPHY OF NEW BRITAIN BOTANY.
1. Baxer, J.G. A Summary of New Ferns, 1874-91. Anns. of
Bot. v. (1891), p. 480.
11. Bockener, O. Die auf d. Expedition S.M.S. ‘Gazelle’ gesam-
melten Cyperaceen. Engler’s Bot. Jahrb. v. (1884), p. 89.
11. Eneurer, A. Die auf d. Expedition 8.M.S. ‘Gazelle’ gesam-
melten Siphogamen. Engler’s Bot. Jahrb. vir. (1886), p. 444.
1 Clarke, ‘“‘ Cyrtandree”’ in De Candolle’s Monographie Phanerogamarum, v.
1883, p. 145.
1896.] from New Britain (Neu Pommern). 97
Iv. Hackent, E. Die auf d. Expedition 8.M.S, ‘Gazelle’ gesam-
melten Gramineen. LEngler’s Bot. Jahrb. vi. (1885), p. 233.
v. Hennines, P. Fungi novo-guineenses. 11, Engler’s Bot. Jahrb.
xvull. (1894), Beibl. 44, p. 22.
vi. Linpau, G. Acanthacee papuane. Engler’s Bot. Jahrb. x1x.
(1894), Beibl. 48, p. 3.
vi. MueEwuer, F. v. Description of a species of Eucalyptus from
New Britain. Australian Journ. of Pharm. 1886. July.
VIII Two new species of Sterculia discovered by R. Parkinson
in New Britain. Australian Journ. of Pharm. 1887. Feb.
Ix. -———- Descriptive notes on Papuan plants. v. Melbourne,
1878.
x, Mutter, J. Die auf d. Expedition d. Gazelle gesammelten
Flechten. Engler’s Bot. Jahrb. 1v. (1883), p. 53.
x1. Naumann, W. O. Vegetationscharakter d. Inseln d. Neu-
Britannischen Archipel u. d. Insel Bougainville. Engler’s
Bot. Jahrb. vi. (1885), p. 422.
xu. Parkinson, R. Im Bismarck Archipel. Leipzig, 1887.
xin, Preit,G. J. Land u. Volk in d. Bismarck Archipel. Verhandl.
d. Ges. fiir Erdkunde zu Berlin, xvii. (1890), p. 144.
xiv. Powerit, W. Wanderings in a wild country. London, 1884.
xv. Scuumann, K. Die Flora d. deutschen ost-asiatischen Schutz-
gebietes. Engler’s Bot. Jahrb. 1x. (1888), p. 189.
xvi. Stuper, T. Ein Besuch auf d. Papua-Inseln nordlich von
Neu-Guinea. Deutsch. geogr. Blatter, 1. Bremen (1877)
p. 182.
xvi. WarsurG, O. Die Flora d. asiatischen Monsungebietes. Ges.
fiir deutsch. Naturf. u. Aerzte. Leipzig, 1890.
Beitrage zur Kenntniss d, papuanischen Flora. Engler’s
Bot, Jahrb. x11. (1891), p. 230.
xix. Askenasy, E., THtmen, F. v., Kunn, F., Encaurer, A., and
others in Forschungsreise 8.M.S. ‘Gazelle’ in den Jahren
1874-76. iv. Berlin, 1889.
Monday, 24 February, 1896.
PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR.
J. Reynolds Green, Se.D., Trinity College; Charles Cave, B.A.,
Trinity College; J. Parkin, B.A., Trinity College, were elected
Fellows of the Society.
The following Communications were made to the Society :
(1) Kaxperiments on Liquid Avr. By Professor DEWAR.
VOL, IX, PART II, 7
98 Mr Brill, On the Generalization of [Feb. 24,
(2) On the Generalization of certain Properties of the Tetra-
hedron. By J. Britt, M.A., St John’s College.
1. Ina paper? published in the Messenger of Mathematics for
last August, I obtained a generalization of some of the properties
of the plane triangle with the aid of ordinary algebra. I now
propose to utilize the theory of binary matrices to obtain a
generalization of the corresponding properties of the Tetrahedron.
The methods used will be found to bear a close analogy to those
used in a paper printed in the sixth volume of the Proceedings of
the Society®.
2. In order to facilitate the working out of the subject, we
will adapt the notation used by Hamilton in his theory of quater-
nions to the theory of binary matrices, which is really the theory
of quaternions in a somewhat different form’®.
Let m be a binary matrix whose characteristic equation is
We will define the operators U and W with the aid of the
equations
Um=x, (WmP=p,
where, for the sake of definiteness, we suppose that Wm represents
the positive value of Vu.
The operator K will be defined by the equation
Km = 2X —m,
so that we have
TO Aes = VAUD apecasebasosesedbecsos: (2).
We also have
m.Km=Km. m= 2\m —m?=p=(Wm)?......-.. (3).
In addition to the above operators, we will introduce an
operator V defined by the equation
m= Um+ Vm,
so that we have
1 «Note on the Application of Analysis to Geometry.” Messenger, xxv. 49—59.
2 « A New Geometrical Interpretation of the Quaternion Analysis.” Proc. Camb.
Phil. Soc., vi. 156—169.
3 It will be seen that K and V correspond to Hamilton’s K and V, while U
coaepene to his S, and W to his T. Hamilton has no symbol corresponding
to L,
1896.] certain Properties of the Tetrahedron. 99
and therefore
(Wm) =m. Km =(Um + Vn) (Um — Vm) = (Um) - (Vm).
Thus we obtain, for the characteristic equation of the matrix
Vm, the equation
(Vmy +(Wmy — (Umy = 0,
from which it follows that
UVm=0, WVm= {(Wmy —(Um)}3........004. (5).
We also have
(Kmy =(Umy — 2UmVm + (Vimy
= 2 (Umy— 2UmVm— (Wm)
= 2UmKm —( Wm),
or (Kmy —2UmKm + (Wm) =0,
from which it follows that
Ran Oni Wk = Witte 2 to area es (6).
Now suppose that we have a second matrix mm’, whose character-
istic equation 1s
DUS —— Pe cole flO acon 5 o'tain tem spe (7).
Then, in addition to equations (1) and (7), we have an equation
involving both m and m’, of the form
mov’ + m'm — 2r’m — 2m’ + 2v=0 1... eee (8).
The equations (1), (7), (8) are said to constitute the catena of
relations satisfied by m and m’.
We will introduce one more symbol L, defined by the equations
dsp, = Li 90S Wises bi4 Werveytaee> Abd. (9).
We have
mKm' +m’ Km = m(2Um' — m') + m' (2Um — m)
= 2mUm’ + 2m’ Um — (mn + m'm)
SS OMAR RS Pie cll acicta de cake anda acnane (10),
by means of equation (8).
In the sequel we shall sometimes be concerned with the matrix
unity. When it is necessary to bring this matrix in evidence we
shall denote it by the symbol w, otherwise we shall treat it in th
customary manner. ‘The said matrix has both its latent root:
equal to unity, and thus we shall have
Uw=1, Ww=1, Ko=o, Vo=0,
Imo = Lom = Um.
~I
|
bo
100 Mr Brill, On the Generalization of [Feb. 24,
The catena of relations satisfied by m and m’ may be written
in the form
m —2mUm +(Wm) = 0,
m?— 2m’ Um’ + (Wm'P= 0,
mm + mm — 2mUm' — 2m’ Um + 2Lmm’ = 0.
From these we may readily deduce the characteristic equation
of a matrix of the form wm+ ym’, where w and y are scalars.
We have
(am + ym’) = am? + vy (mm' + m'm) + ym?
= 2 (am + ym’) (ca@Um + yUm’)
— {a (Wmy + 2eyLmm' + y? (Wm'y}.
Thus we obtain
U (am + ym’) = 2Um + yUm’............... (11),
and, as a special case,
Uaem = «Um.
Thus the operator U is commutative with scalars, and is also
distributive in its operation. It follows from equations (2) and
(4) that the operators K and V possess the same properties.
Further, the formula (11) is capable of generalization by suc-
cessive application, so that we obtain
UxSam=ZaUm, KYam = X«2Km,
Viren Sa Vii ee eee (12).
We also have
{W (am+ ym’)}? = 2 (Wm) + 2ayLmm' + y? (Wim'y.
This equation also may be generalized by means of a property
of the symbol L, which we proceed to develope. We have
20 (2am .m)=(Lam) Km’ +m’ Kam
= La (mKm’ +m’ Km)
= Opals 10), Been ee een (18).
Also, if in (8) we write m’=™m, it reduces to (1), so that we
have
Im? = (Wm).
Thus we obtain
. (Wiamy = L (Samy = alm? + QSaa' Lm’
= 2a? (Wm) + 22ae' Lmim’...(14).
1896.] certain Properties of the Tetrahedron. 101
The characteristic equations of mm’ and m’m may readily be
deduced from the catena of relations satisfied by m and m’. They
will be found to be
(mm) — 2mm’ {2Um Um! — Imm’} + (Wm. Wm')?= 0,
(m'm)? — 2m'm {2UmUm' — Imm’} + (Wm. Wm') = 0.
Hence we have
Umm = Um'm = 2UmUm’ — Imm’ ...........4... (15),
and Ward = Weare = Win WI esac ssxvaneinx Sargon (16).
We must here take notice of a peculiarity of the symbol Z,
which does not belong to the other operative symbols we have
made use of, viz. that L (mm’.m’) is not equivalent to
L(m.m'm’),
nor may we replace L(mm’.w) by Imm’. This is evident from
the definition of Z, and may also be brought out with the aid
of equation (15), which may be made to furnish us with ex-
pressions for the two quantities to be compared.
Finally, we have
Km. Km =(2Um’ — m’)(2Um—m)
=4Um Um’ — 2mUm' —2m'Um+ m'm
= 4UmUm' — 2Lmm' — mm’
=2Umm — mn’
= Kmnv.
3. The matrices that we shall make use of in this paper will,
for the most part, be expressed in a special form. We will suppose
p and q to be two constant matrices satisfying the catena of
relations
ap? — 2hp + b=0,
aq? — 29q+c¢=0,
a (pq + gp) — 29p — 2hg + 2f=0,
where a, b,c, f, g, h are scalar constants; and the matrices with
which we shall be chiefly concerned will be of the form
m=x+ py + QZ,
where w, y, 2 are scalars.
Now we have
aUp=h, aUq=g, a(Wp)=b, a(WaqyP=c,
aLwp =alpwo=aUp=h,
aLwg = algo =aUq=4Q,
alpq = aLqp =f.
102 Mr Brill, On the Generalization of [Feb. 24,
Hence, by means of the first of equations (12), we have
aUm= ax + hy + gz.
From equation (14) we obtain
a (Wm) = aa? + by? + cz + 2fyz + 2gza + 2hey.
If we introduce a second matrix of the given form, viz.
m’ = x + py’ + gz’;
then, with the aid of equation (13), we readily deduce
aLmm' = axa’ + byy’ + ze +f (yz +y'2)
+9 (za +20) +h(ay' +2'y).
4, We now come to the establishment of a connection of our
analysis with geometry. We will suppose in the first place that
our axes of coordinates constitute a right-handed screw system.
Next, we will suppose that we have a set of three points whose
coordinates are (4, Y:, 21), (@2, Yo 22), (Xs, Ys, Zs), and also a second
set whose coordinates are (a, Y1, 21), (25 Yos 2), (#3, Ys, 23). We
will consider these two triads of points as determining two planes ;
and will suppose the origin to be so placed that the cyclical order
of the subscripts given above corresponds, in each instance, to a
right-handed rotation about that normal to the plane of the triad
which is drawn away from the origin. Further, we will write
2X = My “A; 1 ? 2Y= 4, %, 1
?
Uhp Gp ak LEU Peta |
ho, Cap. Ley dee dl
WAS iy Oho loll,
Fis Op.
Gis Ding Ab
and will suppose that X’, Y’, Z’ denote quantities formed in a
similar manner from the coordinates of the points constituting the
second triad.
We will now write
m=X+pY +qZ,
m'= X'+pY'+qZ;
and, then, by means of the results obtained in the last article, we have
a(Wm) = aX?+ bY? + 0Z?4+ 2fYZ+2gZX + 2hXY,
a( Wm’)? =aX"+bY 2+ cZ24+ 2fY'Z! + 2gZ'X’ + 2hX'Y’,
aLmm =aXX'+ bYY'+¢ZZ'+f(YZ' + YZ)
+9 (ZX'+ ZX) +h(XV'+ X’Y).
1896.] certain Properties of the Tetrahedron. 103
We will suppose (a, Y, 2) to be the coordinates of some point
lying on the line of intersection of the two planes defined by our
two triads of points. Then the equation of any plane passing
through the said line of intersection may be written in the form
(# —ao) (X + kX") +(y — yo) V+hY’)
+(2—%4)(Z+k2Z’)=0............. (17).
Now consider the cone
A (@— mY + Bly — yy +O (2-— al + 2F (Cy — yo) (2 — 2)
+ 2G (2—%) (¢ —%) + 2H (a — x) (y—y) =0.....(18),
where
A=be-f?, B=ca-g*, C=ab—h?,
F=gh—af, G=hf—bg, H= fg —ch.
To find the values of k corresponding to the two tangent
_ planes to (18) passing through the line of intersection of the
planes defined by our two triads, we have to express the con-
dition that the normal through (a, y, %) to (17) lies on the
normal cone of (18). This gives us
a(X +khx’Py+b(V+kY'P+e(Z+kZ’y
+ 2f(V+kY’)(Z+kZ’) + 29g (Z+hZ') (X +kX’)
+ 2h(X +kX')\(VY+kY’)=0.
If this be expanded, it will be seen that it can be written in
the form
(Wm) + 2kLimm’ + kh? (War'y? = 0....... 0.00008 (19).
If k, and k, be the roots of (19), we have
2Imm’
pete V Gay:
aS (Wm'y?’
and therefore
1 ((la\* a) Dam _
2 (2) + ~~ Wm. Wm’
Now k,/k, is one of the anharmonic ratios of the set of four
planes constituted by the two planes defined by our two triads
and the two tangent planes to (18) through the edge in which
they meet. If we replace this ratio by the symbol e8, we have
Linn’ = — Wm Wim’ cos @.
104 Mr Brill, On the Generalization of [Feb. 24,
5. Suppose that
(i; Y1> 2), (a, Yr, 2), (5, Ys 23), (Gans Ys; Z,)
denote the coordinates of four points, so situated that the origin of
coordinates lies within the tetrahedron formed by them. We
will write
2X,=| Yo, 2, 1), 2X.=| ys, 4%, 1
Thy iy | Wig) Cio ok
Oh Gy il | Ope Vang
P= Oy Big Il |, 2h =| ty Ao 1! ;
Wey ig 1s Ops Wie. to
by 25 Il (opie Ak |
We will also write Y’s with the same subscripts to denote
what these expressions become when for the 7’s are substituted
the corresponding z’s, and for the z’s the corresponding 2's. Also
we will use Z’s with the same subscripts for the expressions
obtained when for the y’s are substituted the corresponding 2’s,
and for the 2’s the corresponding ys.
In the above it is to be understood, as before, that our axes of
coordinates constitute a right-handed screw system. Also the
corners of the tetrahedron are understood to be so placed that the
cyclical order of the subscripts in the expression for any X is sup-
posed to be that given by a right-handed rotation about the
outward drawn normal to the corresponding face of the tetra-
hedron.
We have
X,4+ X%,4+ X,+ X,=0,
Y,+ Y.4+ Y,+ Y,=0,
1,+ 4,4+ 4,4 Z,=0.
Therefore, if we write
m, =X,+pY,+q4,
m,=X,+pY,+ qh,
m;= X;+pY;4+ qZ;,
m= X,+pV¥,4+94,,
we have
My +s “EN s 1, —\O Pawn caisaeeen aeeecee ee (20).
1896. ] certain Properties of the Tetrahedron. 105
From this we immediately deduce the equation
Km, + Km, + Kim; + Kimg=0 oo. ec eee eee ee (21).
From (20) we have
mKm, + mkm, +mKhm, + m,km, = 0,
and from (21) we deduce
mKm, +m,Km, + mK; + mK, = 0.
Adding these two equations, and making use of equations (3)
and (10), we obtain
(Wm, + Lmym, + Lmyms; + Lnym, = 0... cece (22).
For simplicity we will denote the edges of the tetrahedron by
the symbols (12), (13), (14), (84), (42), (23), the numbers denoting
the subscripts of the coordinates of the points joined by these
edges. We shall also denote the angles of the anharmonic ratios
corresponding to the edges (12), (13), (14), (34), (42), (23) by the
respective symbols a, 8, y, 8, ¢, y. Further, we shall write
aX2+bY2+cZ2+ 2fY,2, +e 297,X + 2hX,Y,= P?,
and shall denote by the symbols Q, R, S the quantities corre-
sponding to P when the subscripts 2, 3, 4 are substituted for the
subscript 1.
This being premised, we immediately obtain for the interpre-
tation of equation (22), the relation
P=Qcos6+ Roos $+ Scos wp.
Similarly we should obtain
Q=Rcosy +8 cosB+P cos @,
R=S cosa + Pcos$+Q cosy,
S=Pcosp+Qcos8 +f cosa.
Eliminating P, = R, S from these four equations, we obtain
lee cos @, cos, cos | =0.
| cos j —1, cosy, cos B
| cos, cosy, —1, cosa
| cosy, ‘cos 8, cosa, —1
Thus the six angles a, 8, y, 8, , w are connected by a relation
exactly similar to Cayley’s relation connecting the dihedral angles
of a tetrahedron.
106 Mr Brill, On the Generalization of [Feb. 24,
If m; be the matrix corresponding to any fifth plane, we readily
obtain from equations (20) and (21) the result
Imm, + Lmm; + Lmym; + Imm; = 0.
Hence if x1, x2, Xs, Xs denote the angles of the anharmonic
ratios corresponding to the respective sets of four planes consti-
tuted by the given plane, one of the faces of the tetrahedron, and
the two tangent planes to (18) through the line in which they
meet, we have
P cos x, + Q cos x. + L cos x, +S cos x, = 0.
6. From equations (20) and (21) we have
mK = (m, + ms + ms) (Km, + Km; + Km,).
Expanding this we obtain
(Wm)? = ( Wm.) + (Wins)? + (Win)? + 2Lmyin,
+ 22mm, + 2Lm,ms,
that is
P= Q?+ B+ 8 — 2RS cos a — 28Q cos B — 2QRK cos x.
Similarly we should obtain
Q = e+ 8? + P?—28P cos vw —2PR cos d — 2RS cos a,
R2= 8 + P?+Q?—2PQ cos 6 — 2QS8 cos B —2SP cos wp,
S= P?+ + R?-—2QR cos y —2RP cos 6 — 2PQ cos 0.
By adding these four relations we obtain a symmetrical rela-
tion, which may be obtained direct from equations (20) and (21) as
follows. We have
(m, + M+ m3 + m,) (Km, + Km, + Km;,+ Km,) = 0,
which on expansion becomes
(Wm)? + (Wm) + (Wms)? + (Wm)? + 2Lmsm, + 2Lmn,
+ 2Imym,; + 2Lm ym, + 2Lnym; + 2Lm,m, = 0.
Interpreting this we have
P24+Q04+ +8 =2RS cosa+28Q cos 8 + 20K cos y
+ 2PQ cos 0+2PR cos d + 2PS cos wp.
We also have a set of equations of the form
(m, + m.) (Kinny + Km) = (ms + ms) (Kim; + Ky).
On expansion this gives
P?+@— 2PQ cos 0= R?+ 8S? — 2RS cosa.
1896.] certain Properties of the Tetrahedron. 107
The other relations of this set are
P?+ R-2PReoos $= 8+ Q? — 28Q cos B,
P? +S — 2PS cosw= Y@ + R?—2QR cos x.
7. If we write down the first three results of Art. 5 in their
symbolical form, we have
(Wm, + Liym, + Lim; + Lm, = 0,
Imm, + (Wm.) + Imm; + Imm, = 0,
Imm; + ILmym; +(Wms;)?+ Lmym, = 0.
From these three equations we readily deduce
(Wmy, Imm, Imym, |+| Lim, Lmm,, Lmygm, | =0.
Imm,, (Wm,), LImyms Imam,, (Wm.?, Lmn,
Imm, Imm, (Wms)? Imm,;, Imm, (Wms)?
Thus, taking account of equation (20), we obtain
| (Wm, Lmm,, Imm,
Imym,, (Wm), Lmzms
Imyn,, Im,m;, (Wms)
=| L(m,+ms+ ms) my, L(m,+m;,+m,)m,, Lm, + ms + m4) ms;
ILmm,, (Win.), Imm,
Imym,, Lmms, (Wms)?
=| (Wm), Lmm, Lmym,
Imym,, (Wm), LIm,ms
Imm, LImm;, (Wms)?
=|(Wm.,), Lmm;, LImyn,
Im.m;, (Wm;,)?, Lmgsm,
Imyn,, Lmgm,, (Wim)
This result may be written in the form
P?| —1, cos @, cosd |=S?| —1, cosy, cos
cos@, —1, cosy cosy, —1, cosa
cos, cosy, —1 cos, cosa, —1
108 Mr Larmor, On the absolute Minimum _ [Feb. 24,
We may also obtain similar relations connecting Q and R with
S. Thus we have
JOE OA A Jao SF 3 | ib eesinn, GOS/S:
cosy, —1, cosa
cos 8, cosa, —1
—1, cosa, cosh
cosa, —1, cos w
cos , cosy, — 1
—1, cosy, cos8|:| —1, cos, cosh
cos, —1, cosé cos @, —1, cosy
cos8, cos@, —1 cos ¢, cosy, —1
(83) On the absolute Minimum of Optical deviation by a Prism.
By J. Larmor, M.A., St John’s College.
When a ray of light crosses a prism in a principal plane, it
is of course well known, and easy to verify graphically, that the
deviation suffered by the ray is least when it crosses the prism
symmetrically. It seems also to be recognized that no deviation
smaller than this can be obtained when the ray does not pass
in a principal plane; though I have not met with any valid
demonstration’ of this result. The following proof may therefore
be worth recording.
The inclinations y and 7’ of an incident and refracted ray to
any plane normal to the refracting surface, for example their
inclinations to the principal plane of the prism, obey the law
of sines
sin» =p Sin 7’.
Hence, after passing across a prism, the emergent ray is in-
clined to the refracting edge at the same angle $a — 7 as was the
incident ray.
When directions are projected on to a spherical surface, let
& represent the direction of the edge of the prism, and P, Q
those of the incident and emergent rays. Then #P and HQ
are each 4a7—7; and if the arcs EPp and HQq are each a
quadrant, p and q will represent the projections of these rays on the
principal plane of the prism.
1 The proof quoted by Czapski, Treatise, p. 156, from Heath, Treatise, p. 31,
does not seem to be valid.
1896.] of Optical deviation by a Prism. 109
These projected rays are refracted across the prism in accord-
ance with the law of sines, the index being not yw but
pcos 7’/cos yn, where sin 7 =p sin 7’.
If D denote the actual deviation PQ, and d the projected de-
viation pq, then, from the isosceles spherical triangle,
sin 4D =sin 3d cos 7.
Thus, of all incident rays which have the same inclination
4a —~7n to the edge of the prism, that one has its projected devia-
tion d, and therefore also its true deviation D, least, whose pro-
jection passes across the prism symmetrically. This least value
is given by the equation
1
ob _p cosy’.
sin 5 (d+ A)= ae sin 5A,
where A is the angle of the prism.
As yw cos7’/cos n is greater than p, it follows that d is greater
than D,, the minimum deviation for an actual ray passing in
the principal plane: but as it is also greater than D, no inference
can be drawn in this way as to the relative magnitudes of D
and D,.
We may however find the absolute minimum of D by com-
paring with one another the rays, corresponding to different
values of », whose projections cross the prism symmetrically. In
the annexed spherical diagram £# represents the edge, N, N’
E
N 0 N’
the normals to the faces, J, J’ the incident and emergent rays,
and #& the ray inside the prism. The pole of VN’ is #, and
EI, EI’ are equal; the symmetry of the projection of the rays
on the plane NN’ requires that ON, ON’ shall be also equal,
110 Mr Seward, Notes on the [Mar. 9,
so that HRO is the plane bisecting the external angle between
the faces. Thus as JJ’ =D, NN’= 4, we have
sn¢D_ sin(@#—7)
sn4A sinr
where 7, r are the angles of incidence and refraction JN, RN.
It is easy to see by geometrical construction that the right-
hand side of this formula increases with vr. It then follows that D
is least when 7 is least, that is, when R is at O: thus the absolute
minimum of deviation belongs to the ray passing in the principal
plane of the prism.
Monday, March 9, 1896.
PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR.
Mr R. Hargreaves, late Fellow of St John’s College, was elected
Fellow of the Society.
The following Communications were made to the Society:
(1) Notes on the Geological History of Monocotyledons. By
A. C. SEWARD, M.A.
In discussing the relative antiquity of the two great divisions of
Angiospermous plants, the statement is commonly made that
Monocotyledons occur in older rocks than those containing the
earliest traces of Dicotyledons.
The evolution of the Angiosperms and the lines of develop-
ment of Monocotyledons and Dicotyledons, are among the most —
interesting botanical problems; and it is of the utmost importance
to critically examine the evidence afforded by paleobotany as
to the order of appearance of these two classes of plants.
Fragments of parallel-vemed leaves and pieces of stem struc-
tures have frequently been described as species of Monocoty-
ledonous genera; such determinations, however, as are based on
mere external and superficial resemblance, cannot as a rule be
accepted as trustworthy.
The cone-like fossils from Jurassic and Lower Cretaceous rocks
described under the generic name Kaidacarpon, and referred to
the Pandanacee on the grounds of a similarity of form and
structure to the inflorescence of recent genera of that family, are
most probably Araucarian cones, and should be placed in the
genus Araucarites.
1896.] Geological History of Monocotyledons. 111
A case in point is the species Kaidacarpon minus Carr. from
the Lower Greensand of Potton; this it is proposed to transfer to
Araucarites.
In the Geological department of the British Museum there
are several specimens of fossil stems discovered many years ago
in the Iguanodon quarry at Maidstone, and named by Konig
Dracena Benstedtir.
The reasons for making use of the recent generic name are
quite inadequate, and it is much more probable that the stems
are Cycadean and not Monocotyledonous. In some species of
Zamia, e.g. Z. Skinneri, Warsz, Z. Loddigesii, Miq. and others
the stem is without the characteristic armour of leaf-bases, and
presents an appearance very similar to that of the Cretaceous
fossils from Maidstone. The pre-Cretaceous, and some of the
Lower Cretaceous fossils described as Monocotyledons, cannot be
quoted as trustworthy evidence bearing on the question of Angio-
spermous development. As yet we are without any definite proof
of the existence of either Monocotyledons or Dicotyledons before
Cretaceous times, and the statement that the former preceded
the latter does not seem to be supported by the facts of palzeo-
botany.
(2) A description of the Crania found at Girton in 1881. By
R. J. Horton-Smitu, B.A., St John’s College.
The following Crania of which a short description is here given
were excavated from the Anglo-Saxon cemetery discovered at
Girton in 1881.
The work of excavation was undertaken by Mr F. J. H. Jenkin-
son, and a description of the results is to be found in the
Journal of the Cambridge Antiquarian Society of that year.
In the cemetery many crania were found, together with a large
amount of pottery of early Anglo-Saxon date.
It would seem that before the Anglo-Saxons made use of this
piece of ground as a cemetery it had been devoted by the Romans
for a similar purpose. This one might have expected, inasmuch
as it lies alongside the old Roman road, and this supposition is
supported by the fact that some Roman cinerary urns were
discovered at a lower level than those of the Anglo-Saxons; and
with these urns were also found a carved lion’s head and a
military torso, both of Roman workmanship.
All the human remains, however, were found with the Anglo-
Saxon urns and other relics, and as no Roman coins were to be
seen with the skeletons, we may fairly presume that the skeletons
112 Mr Horton-Smith, A description of the [ Mar. 9,
belong, not to the Romans, but to the Anglo-Saxon race. This
fixes the earliest possible date of the cemetery at about 410 4.D.,
the year in which the Roman legion were recalled from Britain.
The latest date possible is not so easy to determine, but inasmuch
as no Christian emblems or relics of any description exist in these
graves, we shall not in all probability be wrong in assuming that
the Anglo-Saxons buried here had not been converted to Chris-
tianity. ‘Their conversion took place about 650 A.D.; and hence
the date of this cemetery may be said to lie between the years 410
and 650 A.D.
The importance of these skulls lies in the fact that they help
us to draw the boundary line between the East Anglians and East
Saxons, for we can see by a study of them whether Girton was in
the East Anglian or East Saxon territory. As far as one can
judge from such a limited number of crania as eight—for these
are all that have reached us—I think Girton must be considered
as an Kast Anglian possession.
In a paper to be published shortly in the Journal of the
Anthropological Institute I have given what I consider to be
the typical indices of both the East Anglian and Saxon skulls.
As the paper has not been published yet, 1 may perhaps be
allowed to reproduce them here. By “East Anglian” skulls, I
mean skulls which were found, some at Hauxton, some in Cam-
bridge itself.
re wad iu cs is
3 RODS | acs Ss 3 q
24/8 |e2lsxeleelax SUES iE ES ale S = ae
€Q/4S/SS/S 0180) So (ae Slag 2\oH Soe o| So
Sole |Sslseulsa| 2s o|sAalaisg|ahics oS
Bela lsall@a/Sa| Sa Se slEossesisaag| og
84) = 6364/54/25 |e Fags e eslea4) ge
& Et Ss ES Ibs
a MS Se 195 | eee
East I) 50 *
Anglians| 74 | 71 | 155°) 85 | 96 Eee 56") | 19-78" oe aines
I I) II
Mean of
Girton | 74°4 |72°7| 1410| 81°8 | 95°5 | 48:9 | 56°7*| 90°3*| 77°6* | 124°7*| 108°4
Skulls (?)
* Mean of Male Indices only.
By glancing at the comparative table given above, it will
be seen that the East Anglian skull differs from the Saxon in
being broader, rather more lofty, and of greater capacity. Its
orbital index is higher and, above all, the face of the East Anglians
is distinctly longer than that of the Saxons.
1896.] Crana found at Girton in 1881. 113
In most of these points the skulls found at Girton show a
greater resemblance to the Anglian than to the Saxon type. The
two main exceptions are the cranial capacity and the orbital
index, where they approach the Saxon type: with regard to the
capacity, I would say that the mean index given for these Girton
skulls is very doubtful. I have been able to take the capacities of
no more than four out of these eight skulls, and of these four one
is a female skull. The index given is the mean of the three male
crania, two of which differ widely from the third, while No. 272,
considering it is a female skull, has in reality a very high capacity.
It is therefore quite possible, that if there had been more of these
skulls at my disposal I should have found the mean index to be,
not 1410, but somewhere about 1550. And unsatisfactory also is
the orbital index given. Im all cases I examined both orbits
where it was possible, and the total number examined was ten.
Now considering how widely different the indices are, varying
from 73°7 to 92:1, it is obvious that not much stress can be laid on
the mean index, which comes to 81°8.
Taking all in all, then, I think it may be said that these
crania belong to the East Anglian and not the Saxon race.
Before giving the measurements of the various skulls, I may
perhaps make a few remarks on the peculiarities of each.
No. 267. On the right side the Temporal Bone meets the
Frontal. The supraorbital notches are extremely large, measuring
3 mm. from above downwards and 6 mm. transversely.
No. 268. Most of the Sagittal Suture is synostosed, and the
skull has been posthumously deformed: I have therefore omitted
the indices of this skull, when taking the mean indices of the
series.
No. 269. In this female skull the Metopic Suture persists.
No. 271. This skull belonged to an adult or rather old male:
an epactal bone is present. On the top of the cranium in the
- middle line is to be found an instance of “ prehistoric trephining.”
The hole is just by the bregma. It is of course hard to say with
absolute certainty whether this hole owes its origin to primitive
surgical skill, or not, but there is no doubt that the hole was
made either on purpose or by accident during life, and judging
from the edges it seems probable that the individual survived the
operation some little time.
No. 272. Female skull, contaiming a very large number of
Wormian bones. These are to be found in the squamous and
lambdoidal sutures of both sides and in the coronal suture on
the left side. Epipteric bones exist on either side and the Metopic
Suture persists. \
VOL, IX. PART II. 5
114 Prof. Hughes, [Mar. 9,
x a re = re * 3. w 3 4 g re 3 x g S
3 gfe (ge ts | SS (eS sa eae
par (S| fs| par rm page) |) ears S ‘S| |
a m Sa) Sales iss QU | ee
= Ge lies 2 2 |g |ae|ss3l2s| 33 |S
C oa 80 a) = re} B Sx | Sa z mol ieyaes Sz
° 2, i) S 2 cs Ss ga Sa 5.8 | O98 =|
qq ® an S 5 & 42 ioe a S|) ae | Ae 2 Ss
2 tS) pai | Sn | eal aS
—$—$<$<< | | | ee ee a penne ne ee
Right) Left
267 $ || 75°7 | 73°8 | 1335 | 77°1 | 79 | 95°9 | 48°5 | 56°7 | 90°3 | 82-2 | 130°8 | 107°6
271 $ || 74°3 | 70°4|1525| 779 | 76'2|99 |50 | — | — | 71 __ | 11375 | 106°9
273 i SN 27°9)| 74.9 |) il ee 7397 |. 90° | 4859 | — | —— | 7 556 ie ae
274 d | 73:1 | 737 | 1375) — | 85295-4494 | — | — S19 iza ror are
269 @ || 72°6| 72°9) — | 92°1 | 88°6 | 92°38 | 4776} — | — | 79°5| — | rII't
270 2M 73 Oo) = Se il Papas lpaeny. lhe bac cet) arm e ne =
272 | 2 |] 73°9| 70°4 | 1480 82°4 | 85°3}99 | 49°1)54 | — |73'2| — | 1052
268+ | 3s || 67°7 | — — |771|— |— |42:2)/— | — | 87-2) — —
Mean indices . 72°7 | 1410 81:8 a 8: 6°7*| 90°2* 7 -6*| 124°7*| r08-
of all except 74°4 4 9555) | 429) SO SOS aa 4°7 4
No. 268
+ Posthumously deformed. * Mean of Male Indices only.
(3) On the Recurrence of Ice Ages. By Prof. T. McKenny
HuaGuHeEs, M.A., F.R.S.
Part IV. ON SOME SCRATCHED STONES FROM THE PERMO-CAR-
BONIFEROUS ROCKS OF SOUTH-EASTERN AUSTRALIA AND
THEIR MODE OF OCCURRENCE.
I have on a former occasion? laid before the Society a large
number of sections and specimens bearing upon the question of
the recurrence of ice ages and discussed the inferences which it
appeared to me might be drawn from the evidence. I then
laboured under two difficulties; one was that I had no specimens
to exhibit im illustration of the glaciation of the basin of the
Indian Ocean, and no trustworthy information as to the exact
manner of occurrence of the glaciated rocks in it. The other was
that a plausible and attractive theory referrmg the phenomena to
extra terrestrial causes was in favour and the conclusions I urged
were proportionately depreciated.
Now, however, through the kindness of Professor Edgeworth
David of the University of Sydney I am able to exhibit specimens
of the striated rocks which he obtained from the boulder beds of
South-eastern Australia and photographs of sections in the deposits
in which they were found.
1 Proceedings Camb. Phil. Soc., 1894, Vol. viii., pp. 98 and 219.
1896.] On the Recurrence of Ice Ages. 115
Moreover the chief arguments formerly urged in favour of the
popular astronomical theory have been found to have been based
upon error, and, though some of its supporters still cling to it for
auld lang syne, they are waiting till some new facts may turn up
in support of it. It seems therefore opportune to urge the terres-
trial theory again.
There seems to be an attempt to retreat behind the well-known
fact that ice makes ice, or the cumulative effect of refrigeration,
especially beyond a certain point. But it seems to be forgotten
that this applies equally to terrestrial causes, and that if a moun-
tain range were upheaved, say, a thousand feet above what would
be the estimated snow line for that locality, the existence of that
snow and ice would so lower the temperature that practically the
snow line would creep down far below the altitude estimated from
considerations of latitude, longitude and level only.
Further, I must point out in passing that the demonstration
offered by Professor David does not provide a bill of indemnity for
those who have been claiming credit for the discovery of glacial
beds and have offered in proof only slickensided pebbles and
similar unsatisfactory evidence. At the Geological Society when
Professor David exhibited, among others, these specimens which
he has kindly presented to the Woodwardian Museum, a stone
was exhibited from the Indian boulder beds. This I had no
hesitation in pronouncing to be merely a slickensided pebble,
a view in which Professor David entirely concurred. Dr Heim
has written to me in answer to enquiries I had addressed to him
in regard to the stone I had noticed in the Museum at Zurich and
said to have been found 7n situ in the “ crystalline boulder beds,”
or “palzeozoic glacial bed” in the Salt range of Sandschal in India.
“The striations,” he says, “are different on different distinctly
cornered sides. That is a phenomenon of quite another order
than glacial striation.”
As I have before explained, the character which is most
common in pebbles which have been subjected to crushing action
in a conglomerate, and most clearly distinguishes them from
glacially striated rocks is the manner in which they often appear
to be pinched out and scored in the same direction on both sides
up to the edge; so that, whereas the same set of glacial striz
seldom run far over the margin on the surfaces of any glacial
boulder, and flat sides are the rule, in crushed conglomerates, on
the other hand, the grooves follow the curvature of the stone, and
the edge is sometimes crushed up as if the pebble had been nipped
out.
One of these Australian specimens shows furrows due to the
weathering of the rock along weaker divisional planes, but these
cannot be confounded with the true glacial striz. We may, I
S—2
116 Prof. Hughes, [Mar. 9,
think, reject the possibility of the scratched stones collected by
Professor David being due to earth-movements in a conglomerate.
In order however that we may avoid all possible sources of
error we must consider the curious cases of polished floors and
striated fragments due to landslips. Of these I exhibited
examples! from Wales and the south of England on the former
occasion. The condition of the surfaces would be in many of these
identical with that produced by glacial action. In both cases in
order to produce it the stones must be in contact. The striations
on fragments from landslhps have however a greater tendency
to be parallel, whereas in all glacial boulder clays it is seen that
the direction of the striz has been frequently changed, owing to
the shifting position of the stones as they have been carried
forward in the frozen mass and scrunched against one another on
a far longer journey and over a much more irregular surface than
in the case of landslips.
Heim and Baltzer attach considerable importance to the
difference in character and effect produced by slips of superficial
debris (Schuttstiirze) and falls of solid rock (Felsstiirze), and
Mr Wickham King recalls examples from the Dumberg landslip
near Elm in which the fallen rock produced a bruise from the
force of impact and a groove beyond it where the mass was forced
forward. Heim points out that when the soil is of a clayey nature
the slickensided surface is as smooth as a mirror, with fine
parallel striations in the direction of the movement. A still more
conspicuous polishing of the surface is always produced upon the
solid rock under the slipped mass: and sometimes it is only the
solid rock at the base that is polished. The polished surfaces in
the slipped mass generally occur in the lowest layers, and some-
times, instead of there being one uniform surface so polished, _
there are several such planes succeeding one another at various
angles. These polished surfaces often extend with remarkable
constancy over very wide areas. In the channels cut to carry off
the water under the landslip at Villnockenn on the Bozberg
railway, which was of small vertical descent but of great breadth,
it was possible to trace a perfectly smooth surface polished lke
glass and extending for several hectares (a hectare is something
under 24 acres).
Dr Baltzer mentions that, after the fall and slip of débris at
Bilten, clearly defined striations, caused by the stones in the
sliding mass, were observed on the upper slopes, some of them
running in sinuous curves. He also states that ruts, like those
made by the wheels of a cart, have been observed after a landslip
in the Suabian Alps; and that, after the landslip of Bottstein, the
1 Nos, 32, 33, 41, op. cit. pp. 120, 121.
1896. ] On the Recurrence of Ice Ages. 117
inclined beds of Opalinthusthone, wherever laid bare, were found
to have a perfectly smooth and polished surface’.
If a mass of slipped earth with scratched stones were found
resting on a rounded, smoothed, and striated surface and were
consolidated into a compact rock it might be difficult in sections of
limited extent to feel sure whether we had not before us an
ancient consolidated boulder clay—and, if such a mass were by
any peculiar combination of circumstances transported piecemeal
and the stones scratched by landslips were dropped in clay, so as
to appear as isolated boulders, it would be difficult to pronounce
very positively as to its origin.
But the account given of the mode of occurrence of these
ancient Australian boulder clays makes it extremely improbable
that they can have been produced directly or indirectly by land-
slips. In no case do they appear to have been formed on or near
the flanks of any steep slopes, but when they rest on a rounded and
polished and grooved surface of Archzan or Ordovician rock,
the direction of the striz on the solid floor is always from the
south, showing that the phenomena are not produced by any
merely local agency.
Some of the boulder clays are interstratified in a vast series of
sandstones and conglomerates of marine origin, which attain a
thickness in places of 5000 feet. This also points to some remote
origin and a mode of transport other than currents of water.
The marine deposits in which they occur are identified with
the Glossopteris and Gangamopteris beds of Tasmania, South
Central Africa, India, and Central America. This gives us no data
for an exact correlation with any known horizon in Europe. They
may have been laid down at any time in the vast interval between
the deposit of our newest Carboniferous beds and the first conglo-
merates of the Poikilitic series—a period so vast that it may be
looked upon as comparable with the time that has elapsed from
the age of the New Red to the present day. Those who adopt the
very unsatisfactory name Permo-Carboniferous seem to favour this
view. There are those however who think that some of them may
belong to the same age as part of the Poikilitic or even Jurassic
series. It is clear therefore that in the present state of our
knowledge the occurrence of glacial deposits in these beds lends
us no aid in settling the question of alternate or contemporaneous
glaciation of either hemisphere.
But they do afford very strong evidence in favour of the view
that somehow or another the incoming and disappearance of glacial
conditions is always connected with great earth movements.
Here we have a depth of 5000 feet at least getting silted up
1 « Ueber Bergstiirze in den Alpen.” Neuen Jahrbuch fiir Mineralogie &c, 1875
and footnote.
118 Prof. Hughes, [Mar. 9,
by material carried from adjoining lands where glaciers crept
down valleys to the sea. That cannot have been a country totally
covered with ice and snow, for the glaciers must have passed
through regions where rocks were exposed and broken up into
fragments which fell upon the ice. They must have been long
glaciers, for there are no scratched stones in short glaciers, in which
there is not sufficient time for the fragments to get into the
crevasses and work their way down to the stony mass where alone
striz could be produced.
Besides this there must have been land on which ferns and
other such plants grew.
It is clearly therefore incorrect to speak of the glaciation of
South-eastern Australia. All that has been proved is that some-
where to the south of Australia there was land with glaciers from
the end of which icebergs carrying clay and scratched stones
drifted north. When the water was too shallow to float them they
touched the bottom and grooved the rocks on which they grounded.
Afterwards when the subsidence of the area had gone on and the
water was deeper they melted and dropped their loads over a sea
bottom covered with the débris carried down by torrents from
lands which had not so severe a climate. Far from bemg a
district of ice and snow, South Australia was then deep down
beneath the waters of the sea, with probably a compensating
elevation of the land in the adjoining regions.
Sir John Lubbock? has pointed out that an examination of the
form of continents suggests a great and comparatively recent
submergence of the Southern hemisphere. The long pear-shaped
promontories pointing south, whether continuous as in the case of
Africa or interrupted as in the case of Australia, are according to
this view only the backbones of continents plunged deeper and
deeper under the water as we follow them to the south. This
implies some great earth movement affecting nearly the whole
southern hemisphere. But local conditions must have determined
what exact effect should follow in each area. For instance if there
were an upheaval of 25,000 feet along some transverse fold, would
it make no difference whether that affected a portion of the earth’s
surface which was 20,000 feet deep under water, or already 20,000
feet above the sea level? These are far within observed heights
and depths.
Again, supposing any pull upon earth’s crust, of such a kind as
men have had in their minds when speculating upon the dragging
of the waters of the ocean from one hemisphere to another, were to
tend to pull a portion of the surface out of place would it make no
difference that the trough in which there had been a sea 20,000 feet
1 Nature, 1887. Geographical Journal, Dec. 1896.
1896.] On the Recurrence of Ice Ages. 119
deep was now filled with solid minerals 24 times the specific
gravity of water—all of which had been transferred from an
adjoining continent 20,000 feet high ?
In this connection how suggestive is the fact that “all the
extreme depths in the ocean are near land or shallow water, and
apparently follow the trend of such upheaved parts of the earth’s
crust’.”
It is also worth noting that the deepest depressions yet found
in the ocean, namely, between 30,132 feet and 30,930 feet, were
those proved by Captain Balfour about 500 miles N.E. of New
Zealand along approximately the same belt of latitude as that of
the depression containing glacial deposits in South-eastern
Australia.
If regional movements depend upon terrestrial causes such as
denudation and deposition, and if shrinkage of the nucleus and
astronomical causes determine only the time when the necessary
readjustments shall take effect, it 1s clear that the general con-
tinuity and never the permanence of oceanic and continental
areas must follow as a matter of course. Migration along the
growing land leaves at the end of a long period a record of similar
fauna and flora, continuous, but not contemporaneous. Hence the
difficulty of assigning an exact date to the deposits containing the
wide-spread Glossopteris and Gangamopteris.
Here we have at last exact observations on an ancient glacial
deposit occurring in a region where the conditions are now such
that no glaciation is possible, and we find that no glaciation took
place in that area on the former occasion either, but only that
glaciated stones were carried there.
We have evidence of great earth movements such as would
account for all the phenomena over the whole of that region, even
down to recent times.
It would be well if astronomers and physicists would cease
to consider only the view that the different amount of heat
received from the sun alternately in either hemisphere is
sufficient to account for the variations of climate which have been
experienced by different regions. They are not asked to account
for any deformation of the whole mass of the earth, nor for any
violent dragging of the topographical poles from the ends of the
axis of rotation. What they are now asked to consider is, whether
there are no forces which have a tendency to distort and dislocate
portions of the surface of the crust; forces which shall be always
tending towards a readjustment of equilibrium over those regions
where transference of vast masses of material from one area to
another has deranged it; which shall have some tendency to
1 Wharton, W. 1. L. Nature, Vol. 53, Feb. 27, 1896, p. 393.
120 Prof. Hughes, On some Chipped Flints from [Mar. 9,
produce results upon the great table-lands and protuberant masses
analogous to what are called “marginal effects” in earthquakes ;
which might explain what are called overthrusts, that is, nearly
horizontal slides of masses of rock; it may be where the friction has
been reduced by the liquefication of deep-seated strata when the
pressure is relieved by the pull, or it may be where there already
existed molten lakes below, or where fractured and lubricated
divisional planes occur in the solid rock.
It is a matter of observation that such movements have taken
place. Can they be explained by any well-supported theory of
earth movements which shall be consistent with all the other
operations which we know have been going on ?
If astronomers and physicists would account for the observed
periodicity of earth movements by allowing the sun and moon to
pull the trigger when denudation and deposition with secondary
iternal changes have loaded the gun they would be speculating
along lines suggested by observation from many different points of
view.
(4) On some Chipped Flints from the Plateau Gravel of
Salisbury and elsewhere. By Prof. T. McKenny Huaues, M.A.,
F.RS.
It has long been an accepted fact that flints showing traces
of man’s handiwork are found in river gravels which from their
relation to the physical geography of the district and by the
shells and bones found in them are referred to a very remote
antiquity. These implements are connected by similarity of
form and by the associated remains with others which have been
found in caves, where a much larger and more varied assortment
of remains of human art and appliances have led to the inference
that the man of that period was not at all low down in the scale
of civilization but might be compared rather to the Esquimaux of
to-day.
Seeing therefore that the earliest men of whom we know any-
thing for certain do not exhibit characters pointing to a low stage
of development, we are always looking out for traces of some still
earlier race. Many a time has the discovery been announced and
primeval man been referred further and further back until some
have even assigned a place in this hierarchy to “man’s pre-
cursors.”
I would invite the attention of the Society this evening to the
evidence which has been recently brought forward in support
of the view that among the flints and in the patches of gravel
which occur scattered, both over the beds which rise from below
the chalk, and over Tertiary beds which rest on the chalk, as
well as over the chalk hills themselves, we have evidence of man’s
1896.] the Plateau Gravel of Salisbury and elsewhere. |
work of a much earlier date than that of the river gravels in
which flint implements have long been recognized. It has been
proposed to group these “most ancient stone” implements under
a new name, palzotatoliths, or for shortness, palzotoliths.
The subject falls into two parts, (1) the age and origin of
the beds in which the flints in question are found, and (2) the
character of the flints themselves.
The upper chalk is mostly covered with a thick layer of what
is known as “Clay-with-Flints.” This consists of the insoluble
residue left when, by the action of the surface water charged
with carbonic and other acids, the carbonate of lime has been
removed. But it is generally the lowest part only of this deposit
which is obviously derived directly from the chalk. In it the
flints are not worn nor broken, or, if they have been broken, the
several parts have not been separated, but all the upper part
of the Clay-with-Flints consists of broken and apparently
weathered flints in a matrix of red clay. This can only be ex-
plained on the supposition that there has been a kind of soil-
creep going on for ages. Had it been due to the agency of floods
the stones and clay would have been sorted and the deposit
would have been more or less stratified. The subsidence neces-
sarily accompanying such enormous subterranean denudation
would initiate and keep up the movement of the superficial mass.
A rough measure of the amount of such subterranean denudation
may be obtained by an inspection of the nearest sections of upper
chalk where it will be seen at a glance what an immense thickness
of the chalk with flints would have to be removed to furnish, say,
10 feet of the insoluble residuum. Every here and _ there,
especially on its margin, the clay has been all washed out of
the “ Clay-with-Flints” and carried away, and a universal covering
of white-weathered fragments of flint is distributed all over the
surface. These flints are also on the move. They creep down
the slopes and accumulate on every ledge and terrace. They
more obviously travel down the “dry chalk valleys,” where also
the motion is largely due to subterranean denudation, the water
which runs through the porous gravel removing the soft and
soluble chalk below it and only appearing at the surface in very
wet seasons when there is more water than can pass even through
this very open gravel. If there happen to have been any remnants
of older superficial deposits left on the hill side, they too start as
the underlying chalk gets destroyed, and travel down by all the
processes of soil-creep, finally becoming worked into the general
superficial mass.
When these various deposits come within the action of either
occasional or perennial streams they are handed on more rapidly
and are dropped as ordinary river gravels or silts.
122 Prof. Hughes, On some Chipped Flints from [Mar. 9,
Professor Prestwich’ has given an instance of a sudden out-
wash due to heavy rain. In this way such superficial deposits
have often been carried down and deposited in stratified masses
hanging on the hill side.
The relative levels of these gravels may be complicated by
contemporaneous or subsequent earth movements, but it will be
long before they lose the character they acquired from their
mode of origin, as they consist chiefly of surface-weathered
flints. |
These are all operations going on still, and the recent causes
and effects being obvious, we reason back by analogy to the ex-
planation of the more ancient results. Take such a district as
that between Six Mile Bottom and Linton.
The higher ground, but not the highest only, is covered with
boulder clay. ‘The chalk is rapidly perishing by subterranean
chemical and mechanical erosion. The upper chalk furnished
the flints which creep down hill by various processes, a large
proportion of them being at one time or another exposed on the
surface. Finally on the Six Mile Bottom side they creep down
the long “dry chalk valley” by Lark’s Hall to the railway
station, carrying with them from above fragments out of the
Boulder Clay, and lower down incorporating the remnants of
terraces of river gravel of the age of the Mammoth and Tichorine
Rhinoceros. |
Over the undulating plateau on top, the stony patches creep
outwards and downwards as the inequalities admit of movement.
Down the steep slope by Linton the débris slips fast, overlying
the patches of boulder clay and still older superficial deposits on
the brow of the hill and creeping out over the lower beds of
the chalk. If the outcrop of chalk is beimg eaten back, these
stony masses will by and by lie on isolated hills and old terraces
far out in front of the new chalk escarpment.
In the country round Salisbury we find very similar conditions
prevailing and similar results followmg. There is an extensive
plateau, or rather “plain of marine denudation” over which there
are patches of Tertiary loams We. resting, along the margin of
the Hampshire basin, on the upper or flint-bearing Chalk.
On lower ground along the valleys there are terraces of Mam-
moth gravel. The “trail,” consisting of the sweepings of ancient
and modern surface soils, has in one place crept off the chalk
on to the Tertiary beds, in another has travelled down and got
mixed up with the gravel of the old river terraces, which were
themselves largely made up of still more ancient surface débris,
with a few sarsen stones, black flint pebbles from the lower
' Quart. Journ. Geol. Soc., Vol. xlv. 1889, pp. 278, 279.
1896.] the Plateau Gravel of Salisbury and elsewhere. 123
Tertiary beds, and boulders of various far-travelled rock which
had got distributed over the surface by earlier operations, not
always easy to explain after so many changes have taken place.
It is from one of these patches of gravel, resting on a bed
of sandy loam of Tertiary age, at Alderbury, three miles south
of Salisbury, that most of the flints I now lay before the Society
in illustration of my paper were procured. Some of them were
collected and given to me by Dr Blackmore, who kindly drove
us to the locality and gave us much information about the district.
I exhibit also some of the Kentish paleotoliths of Prof. Prest-
wich and Mr Harrison, kindly lent by Mr Fisher, and some
collected by myself, near Cambridge. The flints and fragments
show evidence of having been long exposed on the surface. The
sandstones are often fretted and eaten away rather than rolled.
Some of the flints have a good coating of soft white silica, from
which the more soluble colloidal portion has been removed, and
they exhibit traces of the innumerable accidental chippings and
crushings and breaking up under the influence of frost and sun
to which surface-flints are liable; while some were deeply stained
by dark red oxide of iron when buried in the gravel into which
they had found their way after they had been long knocked about
and chipped and weathered on the surface of the ground.
It was clear that the particular beds we were examining were
not merely a surface soil formed in place, but a violently trans-
ported drift from a chalk surface covered with weathered flints,
such a deposit in fact as would be carried down a slope of chalk in
storms when the rainfall was greater than the soil could absorb,
and ran off in torrents, tearing up the rubbly disintegrated chalk
and hurrying along the surface soil and flints. In such a case
a chalky gravel is formed with irregular beds of fine marl, the
matrix bemg almost entirely made up of chalk. When this is
afterwards exposed to the slow decomposing action of percolating
waters and the carbonate of lime is carried away, only the in-
soluble flints and sand and iron oxides remain.
Of this we see distinct proofs in the Alderbury beds. The
flints did not all lie as they would in an ordinary river-gravel
with their longer axes horizontal or so inclined as to enable the
mass to offer best resistance to the current, but they were fre-
quently arranged vertically in loops and hollows into which they
had sunk owing to the gradual but irregular removal of the in-
‘cluded masses of chalky material.
In one place I observed that a part of the chalky matrix had
been banded by infiltered iron oxides, so that the iron ran in
wavy lines conforming to the outline of the included fragments.
When the calcareous portion was dissolved away, those stood
out in separate septarian bands of iron oxides.
124 Prof. Hughes, On some Chipped Flints from [Mar. 9,
Mutatis mutandis we may offer the same explanation of the
origin of the superficial deposits along the North Downs of Kent
and of the mode of occurrence of gravels largely derived from
surface flints and from the destruction of the top of the chalk
which occur in that area, not only over the surface of the chalk
itself but over beds which crop out from below the chalk in front
of the great escarpment that overlooks the weald and over the
Tertiary beds which cling to the dip slope of the chalk on the
north as described in the works quoted above.
The reason why it is of the greatest importance to clear up
this question is that, if the views now put forward are correct,
these deposits may be of any age and that they are even being
formed still. Some of the gravels on ledges and terraces, and the
outlying knolls which represent old ledges and terraces, may be
patches of trail or be due to rain-wash and soil-creep which have
used up remnants of older river gravels, while some of them may
be ancient river gravels which have largely if not wholly derived
their material from the surface.
Sometimes it may be possible to refer a given bed to one
or other of these two gravels so different in mode of transport, if
not in the origin of the material.
If many, perhaps most, of the patches in question have been
formed by the local rainwash and soil-creep, the height of the
deposit above the sea or above the existing rivers goes for nothing,
but, if we must suppose that an escarpment has receded far since
it fed the now outlying hills with its débris, we must admit that as
an argument in favour of an enormous lapse of time since the
objects found in the gravel were deposited where now found, or
we must believe in a much more rapid destruction of the chalk
than has been until recently advocated’.
To consider now the character of the flints found on such
surfaces and in such deposits as those just described.
A blow or crush takes off pieces of flint with a bulb of per-
cussion and a conchoidal fracture. Changes of temperature make
it crack and often remove large lenticular flakes which show no
bulb. This is what so commonly spoils flint implements which
have been lying long exposed on the surface of the ground.
None of these operations necessitate the presence of man.
Any movement which would force one flint against the other
would be likely to produce fractures. The stampede of a herd
of oxen or deer must make many a flake and chip the edge of
many a flint.
The whole of the surface from Balsham to Six Mile Bottom
is covered with flints showing every variety of fracture. Most
1-See Howorth, Geol. Mag. Feb. 1896, pp. 58 et seq.
1896.] the Plateau Gravel of Salisbury and elsewhere. 20
of these are broken-up tuberous flints, some few are pieces of
tabular flint, that is, flint which has replaced the chalk along
lines of joint oblique to the bedding and across the bands of
tuberous flints.
Of course the parts of each flint which are most likely to
get chipped are the more exposed points and thinner edges or
the curved margins which would hold a round stone when pressed
into the hollow. Thus we can easily make a selection of forms
which look as if they had got bruised at the point or edge by
being used. We can find many tabular flints which have got
chipped along an exposed corner or edge, many tuberous flints
which fit comfortably into the hand at one end, and have at the
other or on one side a point or edge which has got chipped.
If over such a land surface we have here and there some
unfinished implements and misfits, both paleeolithic and neolithic
as well as recent strike-a-lights, and now and then all get washed
together, or creep down the hill into the same bed of gravel, it
might have been and it has been suggested, that a large number
of the natural pieces of flint owe their chips to their having been
picked up and used by primeval man. The paleotoliths, says
Mr Montgomerie Bell’, “are not shaped into particular forms by
the will and skill of the workman as palzeolithic flints are. They
are chipped flints rather than shaped flints, used tools, not made
tools.” There is now in Jermyn Street a collection of flints, which
I made to illustrate the view that almost all the artificial forms of
implement, certainly all the common ones, were suggested by the
forms into which flint naturally breaks. If there be anything
in this, we might expect to find rude transitional forms among
surface-weathered flints.
The points therefore which I would accentuate are that, unless
the mode of origin by rainwash and soil-creep above described be
borne in mind, these high-level gravels and flints may be referred
by some to a period the remoteness of which is measured by the
time it has taken to cut the valley down or the escarpment back
to the level of the existing rivers or the base of the present slopes ;
that all the specimens I exhibit are natural forms chipped by the
accidents common to all surface-soils; that they are identical with
and represent every type of the paleotoliths upon the character
and mode of occurrence of which the theory of the existence of
man in Britain before the paleolithic age has been founded.
We are all aware that the genuineness of the first found paleeo-
lithic implements was questioned by many who now believe in
them, especially when @ prior? reasons made them doubtful as
to the possibility of such a discovery.
1 Brit. Assoc. Rep., Edinburgh, 1892, Trans. Sects., p. 900.
126 Prof. Thomson & Mr M°Clelland, On the Leakage of [Mar. 9,
But the difficulty of convincing the public or even the scientific
world of the authenticity and genuineness of any of the specimens
was greatly increased by the enormous mass of false or incon-
clusive evidence that was then adduced in favour of the discovery.
Those therefore who believe most firmly that traces of man earlier
than those now known as paleolithic will be found, should be the
most careful in their examination of the evidence adduced while
the enquiry is in progress.
(5) On the Leakage of Electricity through Dielectrics tra-
versed by Réntgen Rays. By Prof. J. J. THomson, M.A., F.RS.,
and J. A. McCLeLLanp, Fellow of the Royal University of
Ireland, Trinity College, Cambridge.
Experiments proving that dielectrics when traversed by
Réntgen rays conduct electricity were described by one of us
in papers read before the Philosophical Society on Jan. 28, 1896,
and before the Royal Society on Feb. 13, 1896. The following
paper contains an account of further experiments made to in-
vestigate the laws governing the passage of electricity through
dielectrics exposed to Réntgen’s rays.
Method of making the Experiments. The induction coil and
the bulb for producing the rays were inclosed in a large iron tank,
fitted with a metallic lid. A small hole was bored in the lid and
the bulb placed underneath this hole. The radiation from the
bulb passed through the hole and fell upon the dielectric whose
conductivity was to be investigated. In the experiments with
gases two different methods were employed; in the first of these,
which we shall call method (A), the lower end of a piece of glass
tubing about 4 cm. in diameter was closed by a piece of thin
sheet aluminium, a paraffin stopper was placed in the upper end
of the tube, a stout metallic rod passed through the paraffin and
supported a metallic disc with its plane parallel to the plate of
aluminium. The rod and disc were connected with one pair of
quadrants of a quadrant electrometer. The plate of aluminium
rested on the iron tank, which was connected with the earth. To
determine the rate of leak through the dielectric the two pairs of
quadrants of the electrometer were connected together and with
one terminal of a battery of small storage cells, the other terminal
of which was connected with the earth. The quadrants of the
electrometer were then disconnected from each other and from the
battery. Before the Réntgen rays were turned on the insulation
was so good that there was no movement of the spot of light
1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 127
reflected from the mirror of the quadrant electrometer, as soon
however as the rays passed through the dielectric there was
leakage through the dielectric, the potential of the disc approached
that of the aluminium plate and the spot of light moved across
the scale. The rate of leak was determined by measuring with a
stop-watch the time taken by the spot of light to pass across
50 scale divisions. The wire attached to the middle of the electro-
meter carried a vane which make the deflections of the electro-
meter dead beat.
In the other method, which we shall call method (B), a mica
window was inserted in the side of a glass vessel shaped like a
lamp-glass, the window was placed opposite to the hole in the
tank containing the coil and bulb. The open ends of the glass
vessel were fitted with paraffin plugs, through each of these plugs a
metal rod passed carrying a metal disc, the two discs were parallel
and opposite the window. As long as the gas between the discs
insulated no electricity could pass from one disc to the other.
One of the discs was kept permanently connected with one
terminal of a battery of small storage cells, the other terminal of
which was connected with the earth, while the other disc was
connected to one pair of quadrants of the electrometer. The
other pair of quadrants were connected to earth. If the two pairs
of quadrants were connected together and then disconnected the
spot of light reflected from the mirror would remain at rest if the
gas between the discs (which are at different potentials) remained
an insulator, when however electricity can leak through the gas
the potentials of the two discs will tend towards equality and the
spot of light will move across the scale. The spot of light
remained at rest when the gas between the plate was not
traversed by the Réntgen rays; as soon however as these passed
through it the spot of light began to move, and the conductivity
of the gas was determined by measuring the time taken for the
spot of light to pass over 50 scale divisions.
Conductivity of different gases when traversed by the Rontgen
rays. The following results were determined by the method A.
The vessel was filled with air at atmospheric pressure and tem-
perature and the rate of leak when the rays were passing through
the air determined. The air was then pumped out and the
vessel filled with the gas to be examined and the rate of leak
again determined; after this the gas was again pumped out and
the vessel refilled with air and another determination of the rate
of leak made; this process was repeated several times.
For these determinations it is necessary to use a bulb whose
rate of emission of the Réntgen rays remains steady. There is
sometimes a little difficulty in getting the bulb into this state,
many bulbs which will produce satisfactory photographs are so
128 Prof. Thomson & Mr M°Clelland, On the Leakage of [Mavr. 9,
variable that they are useless for these measurements. We
generally found that a bulb got steadier after bemg used, indeed
we never found a bulb that was steady enough for our purpose
when first taken off the pump.
The following table contains the rate of leak of different gases
at atmospheric pressure, and unless when otherwise stated at a
temperature of about 15° C., the rate of leak through air at this
temperature and at atmospheric pressure being taken as unity.
Name of Gas. Molecular Weight. Relative rate of Leak.
Hydrogen 2 5
Coal gas 8
Ammonia gas Ih ‘9
Sulphuretted Hydrogen 34 35
Carbonic acid gas 44 12
Sulphur dioxide 64 3
Nitrogen peroxide (N.O,) 92 3
Chlorine 71 12
Bromine (at the temperature
of boiling bromine) 160 9
Iodine (at the temperature
of boiling iodine) 230 7
Hydriodic acid gas 126 +
Mercury vapour (at the tempera-
ture of boiling mercury) 200 10
It will be seen from the preceding table that the electrical
conductivity of the heavier gases when exposed to the Réntgen
rays is greater than that of the lighter gases, the order for
electrical conductivity does not however exactly correspond with
the order of the molecular weight. A very marked feature of the
table is the high conductivity of the halogens, in fact the leakage
of electricity from a charged disc through a tube filled with
chlorine is a very sensitive and convenient measure of the inten-
sity of the Réntgen rays, and was used by us in many of the
experiments described in the later part of this paper.
The high conductivity of mercury vapour is very remarkable,
for this gas only allows the ordinary electric discharge to pass
through with great difficulty, whereas under the influence of the
Roéntgen rays it is one of the best conductors among the gases we
investigated.
In the case of most of the preceding gases the rate of leak was
determined when the charged disc was electrified positively as
well as when it was electrified negatively, but no difference was
ever detected between the rate of leak in the two cases.
1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 129
Influence of pressure on the rate of leak. A series of experi-
ments, using the method A, were made to determine the rates of
leak through air at different pressures. As the following numbers
show, the rate of leak diminishes as the pressure diminishes though
the rate of diminution in the rate of leak is not so rapid as that of
the pressure.
Rate of leak through air at different pressures.
Time in seconds taken for the
Pressure. spot of light to pass over 50 {Pressure}?
scale divisions. x time.
By gy 39 752
Hee 57 655
55 81 600
15 109 422
Second set of experiments.
750 34:5 931
470 41 902
320 51 918
170 74, 962
45 97 650
Rate of leak through sulphuretted hydrogen at different
pressures.
771 15 417
551 18°5 454
341 23°5 454
101 48 480
31 97 533
ile 140 462
Rate of leak through sulphur dioxide at different pressures.
Tol 22 611
501 28 616
291 42 714
150 60 730
| 160 528
VOL, IX. PART II. 9
130 Prof. Thomson & Mr M°Clelland, On the Leakage of (Mar. 9,
Rate of leak through coal-gas at different pressures.
769 58 1606
579 70 1680
374 81 1563
Rate of leak through hydriodic acid gas at different pressures.
769 7 194
489 8'5 189
289 10°5 178
89 20°5 193
These numbers show that over a considerable range of pressures
the rate of leakage through the gas, 2. the electrical conductivity
of the gas, is approximately proportional to the square root of the
pressure. Now we know from the theory of the dissociation of
gases that in cases where the dissociation is small, z.e. where the
number of ions is small compared with the number of the un-
dissociated molecules, the number of ions is proportional to the
square root of the pressure. Hence the results of our experiments
indicate that the electrical conductivity of gases traversed by
the Réntgen rays is proportional to the number of ions, and as
long as the gas and the number of ions is the same is independent
of the number of undissociated molecules, or in other words, the
electrical conductivity is a function of the number of ions and not
of their mean free path.
Effect of temperature upon the conductivity of a gas at con-
stant pressure. A few experiments were made to determine the
effect of temperature upon the conductivity of air at constant
pressure. It was found that the conductivity at high tem-
peratures was slightly less than that at the temperature of the
room.
Further experiments showed that as the gas was heated up
the conductivity attained a maximum value, after which it began
to diminish.
As an instrument for measuring high temperatures was not
available at the time of making these experiments, further
consideration of these effects must be reserved for a future
aper.
Effect of Variation in the Potential Difference on the rate of
leak under the influence of the Réntgen rays. A very remarkable
and characteristic property of the conductivity produced by these
rays in a gas, is that the rate of leak as the potential difference
increases soon reaches a maximum value and becomes almost
independent of the potential difference. Many experiments were
made to investigate this point, using both methods A, B. The
1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 131
following may serve as specimens of such experiments; the method
used was B, and the gas in the tube was air.
Potential difference in volts between Time required to leak through
the discs in the tube. 50 scale divisions.
2 58
+ 44
6 30
8 25
10 25
12 28
16 26
35 26
73 25
108 25
138 24
278 23
Another set of measurements gave, when the gas in the tube
was chlorine,
35 8
75 8
132 7
A third set with a chlorine tube with two sheets of tinfoil
between the exhausted bulb and the discs,
3d 18
75 17
132 15
These numbers show that the rate of leak and the current
through the gas is almost independent of the electromotive
force. If we regard the conduction as electrolytic the gas
being ionised by the Réntgen rays, the fact that the current
is independent of the electromotive force indicates that the
velocity of the ions is independent of this force. This result is
consistent with the law connecting the conductivity with pressure
for we saw that this implied that the conductivity was propor-
tional to the number of ions but independent of their mean free
path. Now if the conductivity depended upon the velocity ac-
quired by the ions under the action of the electromotive force
it would depend upon the coefficient of viscosity between the ions
and the molecules, and hence upon their mean free path. The
current increases with the potential difference when this is small,
but soon attains a maximum value. This effect would result if
the passage of the Réntgen rays through the gas produced chains
132 Prof. Thomson & Mr MClelland, On the Leakage of [Mav. 9,
of molecules or aggregations of some kind in which the component
atoms with their electrical charges could rearrange themselves
with facility; the time 7 required for this rearrangement being
independent of the intensity of the electric field. The effect of
such a rearrangement would be that in a time 7’ a definite
quantity of electricity passed from one end to the other of the
chain of molecules. If these chains of molecules were distributed
in an unpolarized way through the gas their breaking down
would not lead to a current, as as much electricity would pass in
one direction as in the opposite. As soon however as the chains
are polarized there will be a current. Suppose now that these
chains get polarized under the influence of an external electro-
motive force and that the polarization is analogous to that of the
molecular magnets in a piece of soft iron under an external
magnetic field. Then until all the chains get pulled so as to set
in one direction the current will increase with the potential
difference, but as soon as all the chains get pulled into one
direction the current will reach a maximum value and be in-
dependent of the electromotive force.
Rate of leak through solid dielectrics traversed by the Rontgen
rays. Solid dielectrics when traversed by these rays become con-
ductors of electricity, but the conduction through these substances,
inasmuch as it approximately obeys Ohm’s law, differs in one very
important respect from that through gases. The conduction
through solid dielectrics is also remarkable for the extent to which
polarization is developed. If the two discs im method AB are
imbedded in paraffin, and the paraffin when exposed to the
Rontgen rays has a current sent through it, then if the discs are
removed from the battery and connected together, and the paraffin
kept exposed to the rays a current in the opposite direction flows
through the paraffin. If the Réntgen rays are shut off from the
paraffin, the polarization can be kept locked up in this substance
almost indefinitely, and can after any lapse of time be liberated
by again exposing the paraffin to the influence of these rays.
Solid sulphur showed exactly similar polarization effects to those
shown by paraffin.
The amount of this polarization may be realized from the fact
that the times taken to leak through 50 divisions under a constant
electromotive force, were in four consecutive experiments taken
quickly one after another 20, 47,68 and 80 seconds respectively.
In comparing the rates of leak under different electromotive forces,
it is therefore essential to get rid of polarization between each ex-
periment. In the following experiments this condition was care-
fully attended to.
1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 133
Leakage of electricity through paraffin under different electro-
motive forces.
Voltage. Time required to leak through Product of voltage
50 divisions. and time,
278 14 3892
208 21 4368
138 29°5 4071
fs 56°5 4124
35 140 4900
Thus the conduction approximately obeys Ohm’s law.
Leakage through sulphur.
278 10 2780
208 13°5 2808
138 21 2898
73 37 2701
35 67 2345
And again the conductivity approximately obeys Ohm’s laws.
On the law connecting the rate of leak through a dielectric with
the distance of the dielectric from the vacuum tube. In the experi-
ments made to investigate this law, the vacuum tube was placed
immediately behind a small hole in the metal tank enclosing the
coil and tube. Method B was used to measure the rate of leak,
the vessel in which the discs were placed being filled with paraffin,
as the leak through this gas is very rapid.
The bulb used in the experiments (1), (2), (3) below was of the
shape shown in Fig. 1. The distance of the tip of the negative
negative electrode
positive electrode
section of wall of tank
134 Prof. Thomson & Mr M°Clelland, On the Leakage of (Mar. 9,
electrode from A was about 5 centimetres, and the length of the
electrode about 4°5 centimetres. The bulb was placed so that the
negative electrode was perpendicular to the plane of the hole in
the side of the tank, and its prolongation passed through the
centre of the hole. The discs in the chlorine tube were placed
opposite the hole with their planes parallel to the normal to the
plane of the hole.
EXPERIMENT 1.
Distance between the middle of the discs Time in seconds required to leak
and the point A of the bulb. 50 scale divisions.
6-7 3
13°4 6'°5
201 13
26°8 18
40:2 36
53'6 48°5
67 80
The results of these experiments are plotted in the curve in
Fig.2. The abscisse are proportional to the distance of the middle
-—10 0 10 20 30 40 50 60
ieee
Le | ae
Fic. 2.
point of the discs from the point A of the bulb. The ordinates on
the dotted curve are proportional to the time required to leak
50 divisions, those on the continuous curve are proportional to the
square roots of these times. The continuous curve is a straight
line, passing through a point on the axis which corresponds to a
point C, 7 cm. behind A. Hence this experiment shows that the
times required for a given leak are proportional to the squares of
the distance of the discs from C, or that the rate of leak is
inversely proportional to the square of the distance from C. This
suggests that the Réntgen rays originate chiefly in the neighbour-
hood of C. There is no evidence of any coming from the glass in
the neighbourhood of A, though this is brightly phosphorescent.
1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 135
EXPERIMENT 2. (Made on a different day with the same bulb
arranged in the same way as in Experiment 1.)
Distance from centre of the discs to A. Time required to leak 50 divisions.
55 2°5
ue 5
16°5 fi
22 13°25
oN 15a
33 25
38°5 35
The curves plotted in Fig. 3 show the results of these measure-
ments, the ordinates are proportional to the square roots of the
Ere. 3.
times of leak and the abscissee to the distances from O. We see
again that a straight line passing through approximately the same
point as before represents fairly well the relation between the
distance and the square root of the time required to leak 50
divisions. Thus the results obtained by experiments (1), are
confirmed by (2).
EXPERIMENT 3. Same arrangement as before.
Distance of discs from A. Time required to leak 50 divisions.
6°5 less than 2
a5 13
32°5 32
52 61
The results are plotted in Fig. 4, and confirm the conclusion
already drawn. In the next (3) experiments, a tube of another
pattern was used. This is represented in Fig. 5, A is a flat
aluminium plate, B and C aluminium wires fused in the tube.
The dimensions of the tube are marked on the figure. The bulb
was placed so that D was close to the hole. In Experiment 4,
136 Prof. Thomson & Mr M°Clelland, On the Leakage of [Mar. 9,
when the plate A was the positive electrode and the wire B the
negative, the followimg results were obtained.
Fie. 5.
EXPERIMENT 4.
Distance of the centre of the discs from D. Time required to leak 50 divisions.
Ard 6
9 10
13°5 15°5
18 25
22°5 30
27 40
31°5 60
-10 0 10 20 30 40
1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 137
The results are plotted in the curve shown in Fig. 6, where the
ordinates are the square roots of the times and the abscisse the
distance of the centre of the discs from D. We see that the
measurements are represented by a straight line cutting the hori-
zontal axis at a point corresponding to a point in the tube about
6cm. behind D. Thus the rate of leak varies inversely as the square
of the distance from a point distinctly behind the flat aluminium
plate, which in this experiment is used as the positive electrode.
EXPERIMENT 5. In this experiment the same tube was used
as in Experiment 4, but in this case C was the positive electrode,
while B was again the negative electrode. The following results
were obtained.
Distance of centre of discs from D. Time required to leak 50 scale divisions.
4°5 675
9 15)
13°5 29°5
18 545
22°5 $5
Ere. 7.
These results are plotted in the curve shown in Fig. 7, where
the ordinates are proportional to the square roots of the time of
leak and the abscissse proportional to the distances of the centre of
the discs from the point D. The observations are well represented
by a straight line cutting the horizontal axis at a point correspond-
ing to the point in the tube about 35 centimetres behind D. This
poit is very nearly on the flat plate A, so that in this case the rate
of leak varies inversely as the square of the distance from the plate.
EXPERIMENT 6. In this experiment C’ was the negative and
B the positive electrode. The following results were obtained. .
Distance of centre of discs from D. Time required to leak 50 divisions.
6 45
12 ua
18 22
24 33
30 60
VOL. IX. PART I. 10
a
138 Prof. Thomson & Mr M°Clelland, On the Leakage of [Mar. 9,
These results are plotted in the curve shown in Fig. 8, where
the ordinates are proportional to the square roots, times of leak
—10 0 10 20 30
Fic. 8.
and the abscissze proportional to the distances of the centre of the
discs from D. The observations are represented by a straight line
cutting the horizontal axis at a pot corresponding to a point in
the tube about 4 centimetres behind D, and this point is approxi-
mately on the flat plate A and thus in this case as in the preced-
ing, the rate of leak varies inversely as the square of the distance
from the flat plate. Thus reversing the electrodes has produced
no change of the place of origin of the Rontgen rays.
The origin of these rays in these tubes seems to be the flat
plate, though when this is made the positive electrode the origin
seems slightly displaced. To test this point a set of experiments
were made with a tube whose shape and dimensions are shown in
Fig. 9. In the experiments made with this tube the plate was the
Fie. 9.
positive and the wire the negative electrode. The following results
were obtained.
Distance of centre of discs from A. Time required to leak 50 scale divisions.
5 5
10 145
15 23
20 34
25 44-5
1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 139
These results are plotted in the curve shown in Fig. 10. The
ordinates are again proportional to the square roots of the time
and the abscissve to the distances of the centre of the disc from A.
The results are represented by a straight line which cuts the
horizontal axis at a point corresponding to a point in the tube
about 7 centimetres behind A, ze. the rate of leak varies
oy as the square of the distance from a point behind the
plate.
Absorption of the Réntgen rays by sheets of tinfoil. A number
of experiments were made on the effect produced by inserting
between the vacuum tube and the gas exposed to the Réntgen
rays sheets of tinfoil in gradually increasing numbers. The result
of these experiments would seem to indicate that the rays are not
all of one kind, for it was found that the effect produced by the
insertion of a given number of leaves of tinfoil was greater when
the number of leaves already placed between the vacuum tube
and the gas was small than when it was large. This effect would
occur if some of the rays were readily absorbed by the tinfoil,
while others passed through with greater facility. 'Thus when the
rays had already passed through a number of layers of tinfoil
most of the more absorbable rays would be already absorbed, and
any more leaves of tinfoil would only have the less absorbable ones
to deal with. The effect is very marked with some bulbs, though
it is hardly noticeable in others.
We shall first give a specimen of the results obtained with a
bulb showing this effect.
Number of leaves of tinfoil between the Time required to leak through
bulb and the gas. 50 divisions.
0 8
1 10
2 bal
3 11
4, 12
6 16
8 19
10 22,
12 25
16 29
20 36
24 44
28 48
36 60
44 61
Thus to take a few examples, the effect of increasing the
number of leaves from 2 to 10 is to diminish the rate of leak
140 Prof. Thomson & Mr M°Clelland, On Electricity. [Mar. 9, 1896.
“in the proportion of 2 to 1, increasing the number from 12 to 20
decreases it in the proportion of 1°44 to 1, from 20 to 28 m the
-—10 0 10 20 - 30
|
Ere. 10:
a
proportion of 1:33 to 1, from 28 to 36 in the proportion of 1°25 to 1,
and from 36 to 48 only in the proportion of 1:01 to 1.
With this bulb the effect is clearly marked. But im the
following experiments made with another bulb it is much less
noticeable.
Number of leaves of tinfoil between the Time required to leak through
bulb and the gas. 50 divisions.
0 3
2 5
4 8
6 10
8 15
10 20
14 32
18 51
In this case increasing the leaves from 2 to 6 increases the time
of leak in the proportion of 2 to 1, from 6 to 10 in the same pro-
portion, from 10 to 14 in the proportion of 1:6 to 1, and from 18 to
14 again in the same proportion. Thus, though there are traces of
the effect, it 1s not nearly so marked as in the preceding bulbs ;
we therefore conclude that the different rays are emitted by
different bulbs in different proportions. We have always found
this effect most marked in the most efficient bulbs, z.e. the bulbs
which produced the greatest leakage.
We have in conclusion much pleasure in thanking Mr E.
Everett for the assistance he has given us in the preceding ex-
periments. .
PROCEEDINGS
OF THE
Cambridge Philosophical Society,
Monday, 27 April, 1896.
Proressor J. J. THOMSON, PRESIDENT, IN THE CHAIR.
At a meeting held in the University Chemical Laboratory, the
following were elected Fellows of the Society:
Professor J. B. Bradbury, M.D., Downing College.
A. J. Wallis, M.A., Corpus Christi College.
C. T. R. Wilson, M.A., Sidney Sussex College.
The following Communications were made:
(1) On photographing the whole length of a Spectrum at once.
By Pror. LIvEIna.
Professor Liveing exhibited photographs of a variety of spectra
in which the whole length of the spectrum between the wave-
lengths 550 and 214 was depicted on a celluloid film at one
operation. A concave grating of 104 feet radius was used, with
the slit in the centre of curvature, and the slide which held the
sensitive film formed part of a cylinder with a radius of 54 feet,
so that, when the axis of this cylinder was midway between the
slit and grating, every part of the spectrum was perfectly focussed
on the film. The length of the photograph between the limits of
wave-length above-mentioned was 65 centimeters. To obviate
the confusion caused by the overlapping of the spectra of different
orders, he projected on to the slit the image of the source of light
by means of a combination of two quartz lenses with a quartz
prism of 30° between them. The slit being vertical the edge of
the prism was made horizontal, with the result that the more
VOL, UX, PT. LIT, il
142 Prof. Liveing, On photographing a Spectrum. [April 27,
refrangible rays were somewhat diverted downwards, and the image
of the slit produced by them fell on the film at a different level
from that produced by less refrangible rays. Consequently the
spectrum of the second order in the photograph was about half
the length of the lines lower than the part of the spectrum of
the first order at the same place, and the two orders were at once
distinguished.
It is not at all difficult with a table of sines to set out a scale
of wave-lengths for a spectrum formed in this way, and such a
scale once made would of course apply to all photographs taken
with the same instrument, provided there were no inequalities in
the shrinking of the films when drying after development. Un-
fortunately Professor Liveing had found that the films, imelastic
as they seem even when wet, did not shrink uniformly, and he
was therefore turning his attention to glass plates. Glass plates
will not bend to cylinders of so short a radius as 5} feet without
danger of fracture, but thin sheet glass can easily be bent to a
cylinder of double that radius. He was therefore fittimg up a
suitable camera for use with a large grating of 21 feet radius,
and hoped to obtain photographs with it which should not only
be useful for reference, but from which wave-lengths could be
read off to a close approximation. At present he could only read
off wave-lengths from the films by photographing a known spec-
trum, such as that of iron, at the same time and on the same
film as the other spectrum, and measuring the distance of the
unknown line from the nearest lines of known wave-length, a
much more troublesome process than the simple application of a
scale.
(2) On diozymaleic acid and its derwatives. By H. J. H.
FENTON, M.A., Christ’s College.
By oxidation of tartaric acid, in presence of a ferrous salt, a
substance results which has powerful reducing properties, and
which gives a beautiful violet colour with ferric chloride. This
substance has been isolated and proves to be an acid having the
formula C,H,0,. It crystallizes with 2H.,O in flat diamond-shaped
plates, having a pearly lustre. The isolation of the acid was a
matter of extreme difficulty owing to the unstable nature of its
aqueous solution, which decomposes slowly at ordinary tempera-
tures, and very rapidly when heated, giving glycollic aldehyde
and carbon dioxide. Glycollic aldehyde has, in this way, been
isolated as a syrupy liquid; when heated to 100° in a vacuum it
undergoes polymerization, a sweet-tasting solid gum being pro-
duced which has the formula C,H,,0,.
1896.] Mr Fenton, On Dioxymaleic acid and tts derivatives. 143
By oxidation with bromine the original acid is converted
quantitatively into dioxytartaric acid. It is easy to prepare
considerable quantities of free dioxytartaric acid in this way, and
the author suggests the use of this acid as a delicate reagent for
sodium.
The constitution of the original acid has been established by
determination of its molecular weight (in various ways), its
basicity, the behaviour of acetyl chloride, benzoyl chloride, aniline
and other reagents, and by its relation to succinic tartaric and
dioxytartaric acids. It is shewn to be a tetrahydroxylic, dibasic,
unsaturated acid belonging to the maleic series. Its formula is
therefore OH. C.. COOH
|
OH. x1COOH.
By action of hydrogen bromide, an isomeric modification has
been obtained having a distinct crystalline form and yielding a
more stable aniline salt. It is suggested that this may be the
corresponding dioxyfumaric acid.
(3) On the atomic weight of Oxygen. By A. Scott, M.A.,
Trinity College.
Mr Scott gave a short account of the present state of our
knowledge as to the atomic weight of oxygen, and said that it
might be regarded as conclusively proved that if H=1, O=15°87
to 15°88. Morley determined the densities of hydrogen, and
oxygen, the ratios by volume in which the gases combine (by a
somewhat indirect method) and finally combined known weights
of hydrogen and weighed the water produced. Thomsen made
similar determinations but with far less pretension to the highest
accuracy attainable. The results were
Morley. Thomsen.
Weight of a litre of paren
at 0°C. and 760mm. at 1:42900 1°42906
sea level, lat. 45°.
ditto for hydrogen............ ‘089873 089947
Ratio of densities ............ 15°9002 158878
Ratio of combining volumes 1: 200269 1: 2:00237
Atomic weight of oxygen... 15°879 15°869 m0)
The ratios by volume in which the gases combine agree well w
that published by the author directly three years ago, viz.
1 : 2:00245 at about 15°, on
and 1 : 2:00285 at 0°C.
11—2
144 Mr Scott, On Carbon Monoxide and Oxygen. [April 27,
(4) On the combining volumes of Carbon Monoaide and Oxygen.
By A. Scott, M.A., Trinity College.
Mr Scott described some preliminary experiments made to
determine the ratio by volume in which carbon monoxide and
oxygen unite to form carbon dioxide and to determine at the same
time the volume of the latter gas in terms of the others. Experi-
ments so far shewed that the ratio was very nearly 2:1 for the
combining gases, but that satisfactory determinations of the
volume of carbon dioxide produced had not been obtained as yet.
(5) The constituents of Indian hemp resin. By T. H. HASTER-
FIELD, M.A., Clare College, and T. B. Woop, M.A., Caius College.
Cannabis Sativa (syn. indica) is made use of by nearly all the
nations of Southern Asia and Northern Africa on account of the
toxic constituents which it contains. It is stated that the plant
when grown in Europe has no narcotic action, but this statement
requires confirmation. The most common use to which the plant
is put is as a substitute for opium or tobacco amongst smokers,
but sweetmeats, drinks, and pills are also prepared, and all possess
narcotic effects to a greater or less degree. The word Haschish
is generic and applies to any preparation from the hemp plant
ready for immediate use.
Many investigators have already endeavoured to isolate from
the hemp plant the substance to which the characteristic physio-
logical action is due. Amongst the earliest workers in this direction
T. and H. Smith of Edinburgh (1847) should be specially men-
tioned. They prepared a resin from the alcoholic extract of the
plant which produced the effects obtainable from Haschish. At
a later date Personne attributed the effects of Cannabis to volatile
oils; other observers again have stated that alkaloids are present
in the plant but they have not succeeded in shewing that the
alkaloidal substances can produce the same effects as are usually
produced by Haschish. The experiments of the authors have
shewn that the resin of T. and H. Smith contains a large per-
centage of the narcotic constituent, but that the resin itself is
pot a pure chemical compound.
m. That the narcotic constituent is most certainly to be found in
aq? plant resin is emphatically shewn by the fact that the prepa-
tuion which is universally regarded by the natives of India as
and cast powerful and dangerous drug which the plant can yield
isolajning more nor less than the natural resin exuded in large
quantity by the ripe plant but more particularly by the full grown,
unfertilised female plants. To this resin the name “Charas” is
1896.] Messrs Kasterfield and Wood, On Indian hemp resin. 145
given; it is collected by the natives of India, who are said to
walk through the ripe hemp fields dressed in leather jackets to
which the resin adheres. This substance is sold in the bazaars at
about 10 rupees per seer, but only small quantities may be bought
at one time without a special license. The substance is mixed with
tobacco and smoked; it produces almost instant intoxication fol-
lowed by no unpleasant symptoms. One of the most remarkable
points about Cannabis intoxication is the sensation of complete
lack of responsibility which accompanies it, and there is little
doubt that the great popularity of Haschish is due to this fact.
No chemical investigation of Charas has been recorded, and
since the narcotic constituent is so highly concentrated in this
substance it appeared desirable to make a complete examination
of the substance ; the authors would here express their indebted-
ness to Mr C. A. Silberrad of Peterhouse, who has procured for
them a considerable quantity of Charas, and has supplied them
with much information regarding the use of the substance in
India where he is now resident.
Chenucal examination of Charas.
The crude Charas is a substance with a greenish-brown earthy
appearance; held between the fingers 1t becomes intensely sticky;
its smell is highly characteristic. In order to isolate the con-
stituents the Charas was extracted with alcohol, ether, or other
organic solvent, whereby a large quantity of insoluble matter
was separated. The alcoholic solution was concentrated and
eventually submitted to fractional distillation, at first under
atmospheric pressure, and finally in a partial vacuum. By this
treatment the following substances were obtained :—
(a) Insoluble residue. This substance has only been super-
ficially examined; it consists to a very large extent of the hairs
of the hemp plant; it contains upwards of fifty per cent. of ash
and about three per cent. of nitrogen. Systematic examination
for alkaloids gave negative results.
(b) The distillate from the aleoholic extract coming over
below 300° C. at atmospheric pressure.
(c) The portion distilling between 270° and 290° at 15 to
60 mm. pressure.
(d) A small quantity of pitch which was not submitted to
further examination.
Constituents of fraction (b).
Terpene, C,,H,,. By re-fractionation (b) was separated into two-
constituents: one of these boiled between 160° and 180° and came
over for the most part at 165° to 175°; the substance is a terpene.
146 Messrs Easterfield & Wood, On Indian hemp resin. [April 27,
Analysis.
Calculated for
10Ha6 Found
CESS 2 ye 2 ee 87:8
Gale SHEE. AY. 5 eae 12:0
Vapour density.
Calculated Found
68 65
The specific gravity at 17° = 0819.
The substance is laevo-rotary, it forms a mono-hydro-chloride.
Sesqui-terpene, C,;H.,. /
The second substance isolated from fraction (b) boiled at 258°
—259°
Analysis.
Calculated for
Crl tbe Found
Cig 1S Sis Gas teeta ae 87:9
SSeS et eon casas ee ape a 116
Vapour density.
Calculated for
C,;H., Found
102 99°8 and 101°'8
The specific gravity = °898 at 18°.
This compound has been isolated by other observers as a con-
stituent of Personne’s “ Cannabene.”
Constituents of fraction (c).
When fraction (c) was allowed to stand crystals separated ;
these were found to be sparingly soluble in alcohol, and were thus
readily separated. Analysis shewed the substance to be a higher
paraffin, and since the melting and boiling points of the substance
agree with those which can with considerable certainty be pre-
dicted for normal-nona-kosane there is some probability that the
compound is this hydrocarbon.
Analysis.
Calculated for
C,5H 60 Found
Cb Saree tee eee 84:9
1896.] Messrs Easterfield and Wood, On Indian hemp resin. 147
Physical constants.
Calculated for
Oral s Py Found
Melting point = 63—64 ............ 63°5—64
Boiling point) _ 85286 I85—290
at 15 5 mm. ok ee a
Narcotic Red Oil, “Cannabinol,” C,,H.,O,.
This forms more than 96 per cent. of fraction (c); it distilled
constantly at 265°C. (20mm.). Analysis agreed with the formula
© ..u,,0).
Analysis.
Calculated for
C,,H.,0,5 Found
ORE (Ue Seen a 791
|S VESw Cc hemh sss 55 ae 9-0
The figures are the mean of four concordant analyses made
upon different preparations.
The molecular weight by Raoult’s freezing-point method was
found to be 273, the formula C,,H.,O, = 272.
The substance is liquid above 60°C., below that temperature
it is a cherry-red, semi-solid resin. It is insoluble in water, but
dissolves easily in most organic solvents.
The compound yields mon-acetyl and mono-benzoy] derivatives,
both of which can be distilled under diminished pressure ; it is
hence to be regarded as a hydroxy] compound; it yields nitro
and apparently sulphonic derivatives and must therefore be a
closed chain derivative. Further experiments upon the constitution
of this remarkable substance are in progress. The authors propose
the name Cannabinol for the compound.
Cannabinol has been isolated by the authors from all the usual
pharmaceutical preparations of Cannabis Indica. The experiments
of Mr C. R. Marshall, Assistant to the Downing Professor of
Medicine, shew conclusively that the narcotic action of the hemp
plant is to be ascribed to the presence of this compound.
The main results arrived at in the present investigation are
summarised in the subjoined table :
suoqivo-orpAFT
21q 878.1} 1U- TOU
d pus TH WAN
[fozueq-ouo;T
pue
[Aqooe-top,
=
{e) a
/,$1g="SwuIs YEg
“UU 0% 4% OLZ—oG9%
oka = are)
jourqvuueg
ILO pert
aa
“] o8=
‘smIsQgT “Ayo
ONPISEl o[IV[OA-UON
‘dd
ON}IN-IC
|
(.€8%) .066—oE8%
"THU GT 38 “g"g
5, (F9) oF 908-89 “dM
/,GT.="sumis ¢ 4% Ho
unyered SUITEISAX()
“SUIS (G9
“ssord “UU Q9—0Z 1B
0066018 48 eo
°/.% = "SULIs OF
06 S6— 0896 “dL
euedi94-mnbsag
—-
990171981
P2TYSIp wresey9
°/o OT ="SU13 00%
‘7 0008 AO SUI[IOg
*/[oG-T = SUuI3 0g
o08T— 0ST “d'£
euediay,
—————|
SloS: GIN
°/o Lp = 10948 SULeIBEAO *fo8g=
*lo88 =‘sur13 eG),
10q}0 UL Tea: anpisery
qsy
SOI] G—SeIVyO
1896.] Mr Marshall, Pharmacological action of cannabis resin. 149
(6) Note on the pharmacological action of cannabis resin. By
C. R. Marsuatt, M.B, (Vict.), Assistant to the Downing Professor
of Medicine.
The pure products: isolated by Messrs Easterfield and Wood
were passed on to me for pharmacological investigation. They
included the resin cannabinol, the terpenes, and a small quantity
of the residue. As it was probable that the active principle lay
in the resin, my attention was first turned to this body: a few
experiments were made on animals and afterwards I took some
myself. The effects produced were similar to those described by
other observers as resulting from the crude drug. These did not
occur after the use of the other substances, and it therefore seems
probable that the effects of the hemp plant are due to the canna-
binol which it contains. This is further supported by the fact
that Messrs Easterfield and Wood have shewn that cannabinol
exists in charas (the most potent of cannabis compounds) to the
extent of 33 per cent., and that it can be obtained, in amounts
varying with the activity, from all the cannabis preparations they
have examined. In this communication I merely wish to establish
the activity of cannabinol, and I shall therefore confine myself to a
description of its effects without commenting upon it further.
I was under the impression that I had taken a small dose of
impure cannabinol sometime previously without any result, so,
about 2°30 on the afternoon of Feb. 19 last, whilst engaged in
putting up an apparatus for the distillation of zine ethyl, I took
‘l g— 15 g. of the pure substance from the end of a glass rod.
The substance very gradually dissolved in my mouth, it possessed
a peculiar pungent aromatic and slightly bitter taste, and
seemed after some time to produce slight anesthesia of the mucous
membrane covering the tongue and fauces. I forgot all about it
and went on with my work; but soon after the zinc ethyl had
commenced to distil—about 3:15—I suddenly felt a peculiar
dryness in the mouth, apparently due to an increased viscidity of
the saliva. This was quickly followed by paresthesia and weak-
ness in the legs. Gradually my mental power diminished—I was
no longer able to control the steps of the operation and com-
menced to wander aimlessly about the room. I had the most
irresistible tendency to laugh; everything seemed ridiculously
funny. At times I felt more rational; but these lucid intervals
gradually grew shorter and I fell under the full influence of the
drug.
i was now in a condition of acute intoxication : my speech was
slurring; my gait ataxic. I was free from all sense of care and
worry and consequently felt extremely happy. Fits of laughter
150 Mr Marshall, Note on cannabis resin. [April 27,
occurred, especially at first, and sometimes the muscles of my face
were drawn to an almost painful degree. The most peculiar effect
was a complete loss of time relation: time seemed to have no
existence. I was constantly taking out my watch thinking that
hours must have passed, whereas only a few minutes had elapsed.
This I believe was due to a complete loss of memory for recent
events. The occurrence of lucid intervals was also peculiar in
many ways. They seemed to come on suddenly, sometimes, but
not always, as if the result of an effort of the will; they lasted a
variable time, being shortest when the symptoms of intoxication
were most marked; and in them I could converse in a rational
manner and even direct the work of the laboratory to a certain
extent. Except in a few instances I do not remember falling
under the full influence of the drug again. About 6 o’clock I had
two cups of coffee and afterwards feeling somewhat better walked
home. The fresh air and exertion revived me. I ate a good
dinner, afterwards read a little, and retired to bed at 11 o'clock
without having experienced any symptoms of sleepiness.
During the action of the cannabinol my pulse rose from 60 to 96
per minute; sensibility as determined by pinching was blunted;
and my appearance was described as “ashy pale.” The pupils
were dilated somewhat, but throughout reacted well to hight and
accommodation. At no time do I remember having had any hallu-
cinations ; no unpleasant after-effects were experienced ; and the
substance seems to possess no constipating action.
Smaller doses produced similar though less marked effects;
with doses of less than ‘01 g. no distinct action was obtained.
Monday, 11 May, 1896.
PRoFEssoR J. J. THOMSON, PRESIDENT, IN THE CHAIR.
The following communications were made to the Society :
(1) Note on the formation of the germinal layers in Amphioxus.
By E. W. Mac Bripg, M.A., Fellow of St John’s College.
The account of the early development of Amphioxus incor-
porated in text-books is due to Hatschek (“Studien iiber die
Entwicklung des Amphioxus,” Arb. Zool. Inst. Wien, 1881). Briefly
summarized it is as follows: the segmentation of the egg results
in the formation of a regular blastula, which becomes converted
into a gastrula by regular embolic invagination. The mesoblast
1896.) Mr Mac Bride, Germinal Layers in Amphiouvus. 151
y yp
arises aS successive pairs of hollow diverticula of the gut, each of
which gives rise to an adult myomere. When about half-a-dozen
pairs of somites have been formed the most anterior part of the
gut buds off two forwardly directed diverticula, which are at first
symmetrically placed and equal to one another, but of which later
the left becomes a small thick-walled pouch, which acquires an
opening to the exterior. The right on the other hand is converted
into a thin-walled vesicle, which extends forward and constitutes
the cavity of the snout.
When rather more than a dozen somites have been formed the
remainder no longer arise as outgrowths of the gut, since a dorso-
lateral fold of the alimentary canal (by the division of which the
first somites were formed) becomes now completely separated from
the rest of the alimentary tract and constitutes a kind of primitive
streak, out of which the remaining somites are formed.
Quite recently Basilius Lwoff (“Die Bildung der primiren
Keimblatter und die Entstehung der Chorda und des Mesoderms
ber den Wirbelthieren,” Bull. de Moscou, 1894) has given a
divergent account of the early development of Amphioxus. Ac-
cording to him the mesoblast is a dorso-lateral solid outgrowth of
the gut, in which the ceelomic spaces (cavities of the myomeres)
appear later as secondary splits: it is true that the pressure of
the notochord on the mid-dorsal wall of the gut depresses it and
raises up the sides as two folds, but these have nothing to do with
the formation of the ccelom.
The development of Amphioxus is exceedingly important from
a theoretical point of view, since in it we meet with the only
instance of a Vertebrate egg (outside the secondarily modified
eggs of the Mammalia), where the yolk is small in quantity and
evenly distributed, and where consequently the early developmental
processes are not impeded by its presence. Hence it is necessary
to interpret the development of other Vertebrates in terms of the
development of Amphioxus, and not vice versé: and in view of
this consideration, and also of the doubt in which Lwoff’s paper
had enveloped our ideas on the subject of the formation of the
layers, I undertook a reinvestigation of the whole subject, and
hope to be able to publish my completed results this autumn. I
am greatly indebted to Mr Sedgwick for placing at my disposal
a large amount of valuable material collected in Sicily by himself
in 1889 and by Mr Willey in 1890.
If we examine a section of a just completed gastrula we ob-
serve that it is roughly triangular in shape with the apex directed
ventrally, and that each of the lateral angles is produced into a
hollow ridge. In a slightly later stage we find that the cavity of
this ridge is shut off from the enteric space in front, whereas
behind it still opens into it. In a still later stage we find the
172 Mr Mac Bride, Note on the formation of [May 11,
same appearance as before posteriorly and also in the most anterior
sections: but between there is a place where the lumen has become
obliterated, so that the front part of the cavity has now no connec-
tion with the hinder part, and thus from a forwardly-directed hollow
diverticulum of the gut a mesoblastic somite has been cut off.
As the larva grows in length this hollow diverticulum grows also,
and from its anterior end a succession of somites are segmented
off. In the meantime however, owing to the consumption of the
yolk, the larva has diminished very much in diameter, and the
cavity of the groove which we may term the ccelomic groove has
disappeared owing to the apposition of its opposite walls; conse-
quently it appears as a solid outgrowth of the gut-wall, with
which however it does not, so far as I have seen, lose its con-
nection.
The mesoblast of Amphioxus may thus be said to originate as
one pair of pouches, opening into the gut behind, which gradually
become divided into somites; and it 1s of great interest to notice
that according to recent investigations this is true also of the
lower Reptilia. (Will, ‘‘Zusammenfassende Uebersicht,’ Zool.
Centralblatt, April 15, 1894.) The vesicles, however, which later
become the first pair of myomeres have a different origin. They
arise as an independent pair of gut pouches situated anterior to
the pouches we have just been considering, and placed also nearer
the middle line; that on the left side retains for some time its
connection with the gut; and although later the continuity of the
two lumina ceases to be observable, owing no doubt to the same
cause as that which obliterates the lumen of the ccelomic groove,
the continuity of the gut and somite walls is traceable in all the
stages I have as yet examined. As Hatschek’s “nephridium” is
found in precisely the same position in the later larva as this
neck of communication between the left anterior somite and the
gut, I have no doubt that the two structures are identical. The
tube known as Hatschek’s nephridium is placed in front of the
mouth in a horizontal position, and Van Wijhe (“Ueber Am-
phioxus,” Anat. Anz., 1893) has found that it communicates with
the gut; this observation I can confirm, and can add that at
its anterior end it opens into the left anterior somite. Van Wijhe
imagined that it was derived from the connection between the
gut and the left of those anterior outgrowths from the gut,
described by Hatschek, which we may term head-cavities; but
these latter soon lose all trace of their primitive communication
with the gut.
On reviewing the facts now related we see first that the
ecelom of Amphioxus is an indubitable enteroccele, and secondly
that the formation of the mesoblast in this animal is easily refer-
able to the type which Bateson has described in the case of
1896.] the germinal layers in Amphioxus. 153
Balanoglossus (Q. J. M. S., 1884). The head cavities represent
the proboscis cavity, the first myomeres the collar cavities, and
the great posterior mesoblastic pouch which becomes segmented
into somites the trunk cavity.
ZoonocicaL LABORATORY,
May 15, 1896.
(2) Note on the continuity of Mesenchyme cells in Echinid
larve. By E. W. Mac Brive, M.A., Fellow of St John’s College.
About a year and a half ago Mr Sedgwick read a paper before
this Society (“On the Inadequacy of the Cell-theory and on the
Development of Nerves,’ A. Sedgwick, Proc. Camb. Phil. Soc.,
Vol. virt., Part rv.) in which he strongly insisted on the view that
free stellate mesoblast cells such as are commonly figured are
not to be found in the Elasmobranch embryo, but that the
appearances thus interpreted were really only the thickened nodes
of a protoplasmic network.
Last vacation I had the opportunity of examining numerous
larve of Echinus esculentus, and my observations support those
of Mr Sedgwick in a very striking manner.
The larvee specially referred to were in the gastrula stage and
possessed a comparatively narrow alimentary tract, outside which
was a wide blastoceele or primary body cavity; and in this latter
were numerous mesenchyme cells.
These mesenchyme cells were of two main kinds: (1) aggre-
gated masses of rounded cells, which formed the matrix of the
future larval skeleton, (2) wandering cells or amcebocytes. Of
these latter again there were two varieties, of which the first were
obviously stellate in form and connected with each other and the
walls of the blastoccele by long processes. This kind of cell has
been seen and figured by Théel (“The Development of Echino-
cyamus pusillus,” Hjalmar Théel, Royal Soc. Upsala, 1892), who
however regarded the union of the processes of these stellate cells
as a secondary phenomenon.
The second kind of wandering cell is rounded in form, and is
in fact precisely similar to the Amoebocyte familiar to all who
have studied Echinoderm anatomy. It has always been described
and figured as if it were perfectly free: yet 1f one examines a
slightly compressed living gastrula of Kchinus esculentus one
observes that these rounded cells, which at first sight look as if
they were completely free, are in every case connected either with
neighbouring cells or with the walls of the blastoccele by exces-
sively fine threads along which they apparently travel.
154 Mr Mac Bride, Mesenchyme cells in Echinid larve. [May 11,
Whilst not wishing to go so far as Mr Sedgwick in denying
reality to the conception of the cell, I am inclined to hold that
the cell structure of the Metazoa is largely due to secondary
differentiation, and that a multinucleate Protozoon like Actino-
spherium is to be compared to the Metazoon body, and not to a
single unit of the same.
(83) Crania from Tenerife. By F. C. SHRUBSALL, B.A.,
Clare College.
When engaged in a course of study at the Vesalianum at
Basel, Professor Kollmann poimted out the importance of the
Guanches and advised a detailed examination of that race if ever
an occasion should offer. This spring, having to spend a short
time in Teneriffe, I gladly availed myself of the opportunity to
measure and describe all the Guanche skulls of whose existence
I could learn in the island. I first examined those in the pos-
session of the British Vice-consul, and afterwards worked at
various private collections, both im Santa Cruz and Orotava,
besides which I have measured the crania in the Vesalianum at
Basel, those in the Anatomical museum at Cambridge, and those
in the museum of the Royal College of Surgeons, London. To the
owners and curators of these collections I must return my sincere
thanks for the great kindness and courtesy with which they gave
me every facility in their power for my study.
Altogether I have examined 54 male and 39 female skulls, and
some 200 long bones, while in the seriations at the end of the
paper I have included the various indices of the skulls in the
collection from the Canary archipelago at Las Palmas, a printed
copy of the measurements of which was lent me by Don Ramon
Gomez of Puerto-Orotava.
The following are the details of the examination :
Cranium.
On taking the cranial capacity of skulls from Teneriffe it is at
once apparent that while they can roughly be divided into two
series, the large and the small, the classification thus established
does not extend to other features, all the variations of face and
cranium hereinafter to be described being found in either series.
The average capacity of the large male skulls is 1550 cc. (maximum
1600 cc., minimum 1425 cc.), while that of the series of small male
skulls is 1180 ce. (maximum 1250 cc., minimum 1155 cc.). The
total mean of the male skulls is 1451 ce., and the average capacity
of the females is 1875 cc., a mean sexual difference of 75 ce. or 75
of capacity. This at first sight anomalous result being doubtless
1896.] Mr Shrubsall, Crania from Teneriffe. 155
due to the fact that all the female crania available for the purpose
of this measurement belonged to the type of large skulls. On
seriating the table of capacities maxima appear on the curve at
- 1525 and 1160, shewing the existence of the two series. The
mean capacity of male skulls from Teneriffe is given by Verneau
as 1672 cc. and by Flower as 1426. Comparing the capacity of
these crania with that of other representatives of the Mediterranean
race we have
Cromagnon, No. 1, 1590,
Solutré, No. 5, 1500,
Caverne de L’Homme Mort, 1606,
Grotte Baye, 1534,
Basques, 1564,
Teneriffan (excluding small skulls), 1550.
Crania from Teneriffe are on the average long and fairly broad,
the greatest transverse diameter being usually bitemporal and
the length being due to development of the occipital region.
The average length of male skulls is 181 mm., and the average
breadth 139 mm., giving a mean cephalic breadth imdex of 76°8,
while in females the average length 178 mm. and the average
breadth 139 mm., giving an index of 78:1; the mean index for
males and females combined being 77°3.
Comparing this with the mean indices of crania from the
different islands of the Canary archipelago as represented in the
museum at Las Palmas and with other races, we have
Teneriffe, 78
aa are i os mean for the whole archipelago, 76°3,
Hierro, 73:2
Caverne de L’Homme Mort, 73:2,
Grotte de Baye, 78,
Spanish Basques, 77°6.
These figures shew a general relationship between the Cro-
magnon race and the former inhabitants of Teneriffe, which is
further brought out by a comparative seriation of the cephalic
indices of adult skulls.
[May 11,
Mr Shrubsall, Crania from Teneriffe.
156
So[BUla,T
BIOULOL)
SO[BULIT
Areweg
purty
OS OS OS BP ee | maa
Sa[vUle T
aye J,
Lael OO 4 6 OH OO b= C/E iS
SOTVUA,T ® SOTRIAT
‘osejediyory
Oo Hon last of os]
AeUBQ = *UOT}D2T Sse = of Se Sec ee
-[OD svueg sary
se) = OIE BHODAAHANA
ysruedg ie we
\IOJ[ OULULO FT
ap ou1eAeD mam NOOO MS AN
Osvedrqo1y
d CO ANDROHNAMMODAHH AN
1¥40.L ANAANAN
BLIULOY) | 4 OHH OMDOMHMANH A
Areue
@) + HANIARMMOMOANA
purty
ayiaauey, | Teeter eit Nee Seat eC. Sh Se
Xopuy DRHOFAMHIDOnRDAROHANOH
OOM rerererererrnnnno
classifying the indices
Comparisons are also furthered by
according to Brocas divisions.
Table of Percentages of Cephalic Index.
osvjedipor1y
> SMHS
an 10 GD k= 0 oO
= ANE | AAA
3
xy 5 6 6 O> ~ H
BOUL Ornron
LOS OPS |
osejediyo1y SHO O19 69
e410 aDaOOs
n TOL oD oO
g
ES
a D010
RSOBEN G OA 619
Sug AN
NvIu.1d A > OH
‘setoueny) I~ ODD
n oo SH ro
o
ee —
3s
= paelery ‘eavyo19
qe ATVNSSQ WOT
ST[MYS Uropojy
QO OH
1d Nr
oO
Of} (2)
es ee
ae a
eicl ee
3 lS Oe
eo 85
aos sig
@ iS} ISI 4
OS era FF
S985
(SB) © i (Ss
aa gals
Begcs
as Qe &
Hnane
1896.] Mr Shrubsall, Crania from Teneriffe. 157
The wide range covered by the indices, viz. 13 units both in
male and female skulls is sufficient to indicate a mixture of races,
while the foregoing table shews that comparative uniformity
must have existed at the time of the Spanish conquest of the
Canaries.
With regard to height, the skulls in the main are low rather
than high, the mean altitudinal index for males from Teneriffe
being 70°5, and for females 72°2, as against male 72°5, and female
71:9 for the whole archipelago. Contrasting with other series,
we have for males,
Guanches, 705,
Cromagnon, No. 1, 65'3,
Solutré, No. 5, (pre
Caverne de L’Homme Mort, 68°8,
Spanish Basques, 70°7,
Modern Teneriffan, (aoe
and for females,
Guanches, G22,
Grenelle, No. 2, 72,
Solutré, No. 2, 74°6,
again shewing the close resemblance to the Cromagnon race of
the former inhabitants of the archipelago. The division into
classes by the altitudinal index is as follows:
Males Females
Total | | Total
Teneriffe Archi- || Teneriffe Archi-
pelago pelago
Chameecephalic 24:1 18:9 30°8 27°4
Orthocephalic 569 BOs i. 90 58-9
Hypsicephalic 19 21:3 19:2 13:7
1 esos Sete aot ee DL
Contrasting breadth and height, the mean index for male
Teneriffan skulls is 92°9, and for females 92:1. Compare
Cromagnon, 88°6,
Solutré, No. 5, 93°7,
Caverne de L’Homme Mort, 96°4,
Spanish Basques, 92°4.,
VOL. IX. PT, III. 1
158 Mr Shrubsall, Crania from Teneriffe. [May 11,
Classifying by this index according to Brocas divisions, we
obtain the following table:
Males Females
Teneriffe | anes | Teneriffe anes
Akrocephalic 40 28-1 44-4 37°5
Metriocephalic 45°5 45°5 48:1 45°8
Tapeinocephalic 14:5 26-4 7:4 16°7
In the great majority of crania from Teneriffe the frontal
region is well developed, the forehead being full, rounded and
decidedly broad, although in some which constitute a distinct
type by themselves it is low and receding.
The glabella is only moderately prominent, but the superciliary
ridges are well developed even in the female, the subcerebral
curve contributing on the average in the male 23:9 per cent.
and in the female 17-2 per cent. of the total frontal curve.
The frontal eminences are usually prominent but do not reach
to the level of the mid-sagittal line.
The sagittal curve in most typical cases runs uniformly back
to the lambda, but in some crania the annular post coronal
depression of the middle third of the parietal bone described by
M. Vernau is to be seen. This depression, which somewhat
resembles that produced by a bandage tied tightly round the
head during early youth, is, according to that author, not an
artificial deformity but a natural variation in the sagittal curve.
After passing the lambda this curve often shews a distinct flatten-
ing over the upper part of the occipital bone, and when this is
present there is a decided fulness of the whole occipital region,
the projection backwards taking place immediately at the parieto-
occipital suture. From the mion the curve passes sharply down-
wards and forwards to the opisthion, the bone in this region being
flattened and strongly marked by muscular impressions. In
many cases the conceptaculz cerebelli are so far developed that
the skull rests posteriorly upon them rather than upon the mastoid
processes or the occipital condyles. The inferior portion of the
occipital bone is horizontal. The relationships in point of size
of the various portions of the curve are shewn in the following
table, in which they are compared with the length of the total
sagittal curve (= 100):
1896.] Mr Shrubsall, Crania from Teneriffe. 159
Frontal | Parietal | Occipital
Males 30°D 34:4 3
Females 33°7 32°6 3
Making similar comparisons for other curves.
The relation of the supra-auricular to the total transverse
curve (= 100) is in males 65°6 and in females 66°8, while that of
the preauricular to the total horizontal (=100) is for males 47-7
and for females 45:4 as compared with
45°3 in skulls from Caverne de L’ Homme Mort,
and 46°1 in Basques.
However on seriating the results of this last relation, we find
that very few crania present this actual mean relationship but
group themselves round the numbers 41 and 52, indicating a
greater frontal and occipital development respectively.
Viewed in norma occipitalis the skulls are somewhat penta-
gonal in form, but the parietal eminences are not very prominent,
and the greatest transverse diameter in about 80 per cent. of
crania lies between the temporal bones. In the better class of
mummies, presumably those of chieftains of some importance,
there is in several instances, more frequently so than in the less
cared for bodies, a prominent median sagittal ridge along a groove
in which the interparietal suture runs for the posterior half of its
course.
The temporal crest is always well marked both in male and
female crania, the double nature of the ridge being very distinct.
The zygomatic processes are stout, strongly arched outwards and
with a supramastoid ridge usually extending up on to the posterior
inferior angle of the parietal bone.
The pterion is of the ordinary H shape and anomalies are rare
in this situation. In many cases the sphenoid and frontal bones
close behind the external orbital process are markedly bulged
outwards, and in the average among males the transverse diameter
from one pterion to the other is greater than the bistephanic
breadth.
Viewed in norma verticalis the crania are plainly pheenozygous,
and appear either pentagonal or, as in a smaller number of cases,
oval ; a slight projection of the face is also noticeable.
The mean dimensions appear in the following table:
12—2
160 Mr Shrubsall, Crania from Teneriffe. [May 11,
“i Males Females
S| | rs} =
efi | 22 | ose | a=
255 Sy || 255 a
S28) 8S | > eagier
ao ee
|
Minimum Frontal Breadth 95 | 68°3 94 | 67:6
Interpterion Breadth 112). | (80:6) |) (Osea
Bi-stephanic Breadth 111 REY LL 80:6
Bi-asteric Breadth 114 82 1077 em
Maximum Transverse Breadth 139 LOO) || TSoe ue
|
The fronto-zygomatic dex of skulls from Teneriffe is for
males 83°3 and for females 89.
Cf. Caverne de L’Homme Mort, 89:9,
Basques, 91°8,
Grotte de Baye, 83°5.
This series of crania may readily be classified into two groups
according to the complication of their sutures. In the first and
smaller division the sutures are simple and wormian bones the
exception ; while in the second series the sutures, more especially
the lambdoid and coronal, are excessively complicated, while it is
rare to find even the sagittal suture simple and wormian bones
are very common. A persistent metopic suture is to be found in
about 8 per cent. of crania of the second series; it may be com-
plete, or persistent near either the bregma or the glabella, the
latter arrangement being the more frequent.
Synostosis usually commences in the sagittal and lower part
of the coronal sutures; contrary to the usual custom the lambdoid
suture is quite the last to close. M. Verneau indeed describes a
case in which the squamous suture had closed up while the lamb-
doid was still open.
Wormian bones are the rule in the lambdoid suture, the com-
monest arrangement being a series with their long axes nearly
vertical and their short axes arranged along the line of the suture,
the two sides being frequently asymmetrical. There may be a
single ‘os-epactal’ or an ‘os-epactal’ with a small median wormian
bone in front of it.
- Passing on from the study of the cranium to that of the face
we find a considerably greater range of variation, Faces from
1896.] Mr Shrubsall, Crania from Teneriffe. 161
Teneriffe are for the more part orthognathous, broad above, nar-
rowing down in the maxillary and mandibular regions, with low,
broad very rectangular orbits, superciliary ridges well marked
and frontal sinuses capacious and extensive; but one also meets
with skulls presenting the features of long, uniformly narrow,
slightly prognathous faces with high and rounded orbits. The
nose is as a rule straight, prominent and leptorhine, but in other
cases it is platyrhine, and the lower border instead of being
sharply cut, as is typical, may be rounded off or even present
simian grooves. The nasal spine is not prominent. The palate
is of almost all forms and sizes, the most typical being the ellipse,
although the parabolic form is also well represented, the alveolar
border projects forwards and accounts for the slight alveolar sub-
nasal prognathism frequently found in skulls from the Canary
archipelago. The lower jaw is strong, broad at the condyles and
angle, but narrow at the chin. The angle is frequently very
markedly everted, shewing the strength of the muscles, thus
correlating well with the strength of the zygomatic arch and the
great wearing down of the teeth, all bemg doubtless due to the
grinding efforts necessary to masticate the but partially cooked
cereals which constituted then, as now, the staple diet of Teneriffe,
and which also accounts for the frequent traces of alveolar abscess
in Guanche skulls.
The various facial indices are tabulated in order below.
Superior facial index of Broca.
Mean male, 63; female, 65.
In the seriation table of this index the range is from 58—87
(29 units) exhibiting maxima at 62 and 66 for males and at 68 for
females.
Cf. males, Cromagnon, No. 1, 63°4,
Grenelle, 667,
Grotte de Baye, 66°4,
Homme Mort, 67:6,
Basques, 67°8.
females, Grenelle, No. 2, 66°5,
Solutré, No. 2, 66°4.
Upper facial index of Kollmann.
Mean for males, 50°2; mean for females, 47°7.
The skulls therefore lie on the border line of lepto and chame-
prosopy, the percentages in either division being as follows:
162 Mr Shrubsall, Crania from Teneriffe. [May 11,
Males | Females
Teneriffe | }000 | Teneriffe | 310,
Chamezeprosope 499 47:1 82°3 85:7
Leptoprosope 57-1 52°9 16-7 14°3
This shews that while the males tend towards leptoprosopy
the females are almost entirely chameprosopic, and if these
indices are viewed together with the orbital and nasal indices the
very disharmonic nature of the face, more especially in the female
skulls, is at once brought to notice.
The distribution of skulls from Teneriffe among the types of
Prof. Kollmann is shewn by the following table :
| Males | Females
Chameeprosope Dolichocephals 30 15°4
Chameprosope Mesocephals 36°4 38:5
Chameprosope Brachycephals 6:1 23°1
Leptoprosope Dolichocephals iki
Leptoprosope Mesocephals 42-4 15-4
Leptoprosope Brachycephals | lh
|
The mean orbital index is for males 83°6 and for females 87:2.
Seriation of this index shews a range from 68—97 (29 units) with
maxima at 80, 83, and 89.
Cf. Solutré, No.1, 74:3,
Homme Mort, 80,
Grotte de Baye, 81:4,
Spanish Basques, 82°6.
The orbits are frequently asymmetrical, the difference in index
between the right and left sometimes amounting to 3 or 4 units.
The nasal index shews a range from 41—60 with maxima at
45—48 and 52. Mean indices being male 47-6; female 41°5.
Cf. Cromagnon, No. 1, 45:1,
Grenelle, No. 1, 49-2,
Solutré, No. 5, 52°4,
Homme Mort, 454,
Spanish Basques, 43°S.
1896.]
The nasal index of the ancient can be compared with that of the
modern inhabitants of Teneriffe, in whom there is a considerable
admixture of Guanche blood, by means of this table of percentages,
Mr Shrubsall, Crania from Teneriffe.
|
PS ilivilse
~ i= | b= |
[32 Ss
eee Be
s3s <4
SS nes RS:
| np
jo)
Leptorhine 27 44
|_Mesorhine —_ 7 35-4
Platyrhine | 8 20°6
shewing the convergence to a mean type in the modern skull.
The general features of the face can easily be traced in a
combined table of facial, orbital and nasal indices, in which I
compare the results of my measurements in Teneriffe and else-
where with those of the collection of skulls from the whole
archipelago at Las Palmas and with those of M. Verneau in
Teneriffe itself.
Males.
Teneriffe. M. Verneau Teneriffe Archipelago
Wesel culeciiesete | a | 8 |S
Microseme | 25:9 | 55°6 | 74:1 || 38:5 | 48-5 | 50 44-2 | 46°3 | 50°4
Mesoseme af | d0°8 | 18:5 || 34°6 | 31°8 | 32°8 || 22:1 | 33°6 | 38-2
Megaseme | 37 | Vil | 7-4 || 26-9 | 19-7.) 17-2 || 33-7 | 20-1 | 11-4
Females.
Teneriffe. M. Verneau | Teneriffe Archipelago
ell eo) ie ba fc ae Pace |e
Sew Nil Slee vei alae
Microseme) 30 | 42-9 61:5 || 25 | 29 , 39-4 Bee 38 |
Mesoseme | 40 | 28°6 | 30°8 || 33°3 | 25:8 | 30°3 | 27°6 | 30°8 | 38
Megs 30 | 28-6 | 7:7 |] 41-7 | 45-2 | 30:3 || 36-2 39-7| 24 |
164 Mr Shrubsall, Crana from Teneriffe. [May 11,
The palatal index has a range of 61—94 with maxima at 78
and 89, mean index for the series male, 79°3; female, 78°9.
Cf. L’Homme Mort, 72°7,
Spanish Basques, 75-2,
Grotte de Baye, 75°5,
French Basques, 79°6.
Classifying these indices according to Virchow’s divisions we
find among males well represented lepto- and brachystaphylinic
groups with somewhat smaller numbers intermediately.
Males. | Females.
Teneriffe | Archipelago || Teneriffe | Archipelago
|
Leptostaphylin 56°5
59°5 | 98°6 66:2
Mesostaphylin 16:1 Iie I Bir 23:9
Brachystaphylin 27-4 21:4 13°8 9°9
The mandible is characterised by the narrowness of the chin,
the strength of the muscular impressions and alveolar border ; the
eversion of the angle and the prominence of the genial tubercles.
The mean goniozygomatic index is in the male 77:6, and in
the female, 72:5, ef.
Mediterraneans, 77,
Mean European, 77°6,
Arabs, 74:2,
Summing up the results of the foregoing measurements it
appears that four types of skull existed in Teneriffe at a period
anterior to the Spanish invasion.
I. The first and most important type in respect of numbers
presents the features of a capacious skull with moderately pro-
minent glabella and superciliary ridges, a well-developed frontal
region and full rounded forehead. It has a sagittal curve pre-
senting a post coronal depression, a lambdoid flattening and a
great fillmg out and projection of the occipital region of the
cranium, while the greatest breadth is bitemporal. The sutures
are very complicated, metopism is not infrequent and wormian
bones are very prevalent in the lambdoid suture. The face is
short, broad above, narrowed below, orthognathous, with low broad
very rectangular orbits, a leptorhine sharply cut nose, slightly
sunken at the root, an elliptical palate and greatly worn teeth.
1896.] Mr Shrubsall, Crana from Teneriffe. 165
This type, which from its superior numbers and greater prevalence
in Teneriffe than in the other islands of the group is to be
regarded as that of the Guanches, may be shortly described as
mesaticephalic, orthocephalic, orthognathous, microseme, lepto-
rhine and leptostaphylin.
All the succeeding types of skull differ from the above in the
absence of the Jambdoid flattening of the sagittal suture and in
the absence of the fulness and projection of the occipital region.
II. The second type, distinguished by a smaller capacity, a
retreating forehead, greater height of skull and lower cephalic
index combined with simpler sutures, comparative absence of
wormian bones, much stronger muscular impressions, larger mas-
toids, and more prominent inion, is somewhat wedge-shaped when
viewed in norma verticalis. It differs but little from the pre-
ceding in facial features, but has a narrower mandible and a
parabolic palate. This type, which is well represented in Teneriffe
and Hierro, may be described as dolichocephalic, orthocephalic,
mesoseme, leptorhine and brachystaphylin.
III. The third type presents the features of an ovoid skull
of small capacity with glabella, superciliary ridges and parietal
eminences not very prominent, although the greatest transverse
diameter is interparietal. It is dolichocephalic and hypsisteno-
cephalic with a sagittal curve rising directly and uniformly from
the nasion, a face prominent and slightly prognathous, a nose
straight, sharply cut at lower border but not depressed at the
root, orbits high and rounded and a palate decidedly long with
the ends of its dental arcade seldom or never incurved.
This type of skull, found more frequently in Grand Canary
than in Teneriffe, is apparently that described by M. Verneau as
Semitic.
IV. The fourth type is a short broad skull of fair capacity,
with a nose not sharply cut but rounded off at its lower border
and often platyrhine or high mesorhine, with high and rounded
orbits and a palate in some cases long and parabolic, but in a few,
elliptical. This type appears to occur in the N. and E. of Teneriffe
and in Gomera more freely than in the rest of the archipelago.
Long Bones.
As these were only studied in the actual burial caves and their
Vicinity, situations somewhat difficult of access, but a few slight
observations were possible. Taking the bones in order:
The humerus as a rule was strong and well-marked, the deltoid
impression and musculo-spiral groove being especially prominent,
166 Mr Shrubsall, Crania from Teneriffe. [May 11,
the olecranon fossa was frequently perforated (in 23 per cent. of
the bones examined). The average maximum length was in the
male 323 mm. and in the female 304 mm.
The radius and ulna were in most cases strongly marked, but
presented no special features of interest.
Average length, radius male 247 mm., female 232 mm., but,
however, very few examples were measured of the forearm bones
of the latter sex.
Ulna. Male 265 mm., female 243 mm.
The femora were large and strong, deeply marked by muscular
impressions and often pilastered. The average length in the
oblique position with both condyles touching the lower end of the
measuring apparatus was for males 424mm. and for females 414mm.
The tebiae were strong and in some instances platycnemic, the
average length being for males 365 mm. and for females 335 mm.
The jfibulae, which were deeply channelled, were of the mean
length of 352mm. in the case of the male and 331 mm. in that
of the female bones. Calculating the height of the former living
inhabitants from these measurements by means of M. Manouvrier’s
sliding scale it is found to have been 1642 mm. for the males and
1552 mm. for the females. The results from each series of bones
is sShewn in the subjoined table.
Calculated height of living individual in millimetres:
Bone | Male Female
Humerus | 1637 1560
Radius 1666 ==
Ulna | 1668 1578
Femur | 1610 IES SKS |
Tibia 1644 1542
Fibula 1626 1542 |
|
Mean height | 1642 1552
giving a mean sexual difference of 90 mm.
Comparing the mean obtained for Teneriffe with the heights
arrived at by Manouvrier’s scale for the races with which the
crania were compared, we have
Teneriffe, 1642,
Cromagnon, 1750,
L’Homme Mort, 1620,
Grotte de Laugerie, 1650.
1896.] Mr Shrubsall, Crania from Teneriffe. 167
A seriation of the heights computed from bones in Teneriffe
shews a range in the case of males of 1550—1710 (160 units) and
in the case of females of 1460—1660 (200 units) with maxima at
1640 and 1550 respectively: this range is sufficient to indicate a
probable original mixture of tall and short races, although it is
clear from historical evidence that the height was fairly even
throughout the island at the time of the Spanish invasion and
that the Guanches were tall.
In an attempt to reconstruct the features of the former in-
habitants we draw our evidence from three sources, the present
population, the chronicles of the Spanish invasion and such ancient
records of the history of the island as we possess.
Turning to the first, we find congregated in and near the towns
on the north and east people with olive skins, dark eyes and black
or dark brown hair, obviously of Spanish descent; lying further
out and distributed in the country districts throughout the island
is a fairer complexioned, brown eyed, chestnut haired race mixed
among whom are isolated families of the former type, while in the
rugged and less easily accessible southern side where the Guanches
last held out and where their descendants are still supposed to
remain in the greatest purity, there are many of fair complexion,
blue eyes and fair or flaxen hair and golden haired children are
quite common. From the second source we learn that many of
the inhabitants of the north of the island at the time of the
invasion were fairer than the Spaniards, although some of those
in the South were dark, while the native records tell the ad-
ventures of a golden haired blue-eyed princess. When added to
this we find in many mummies a profusion of short yellow hair,
although this latter evidence is not strictly admissible owing to
post mortem changes, there is some reason for concluding that at
any rate one race in the island presented the features of a fair
complexion, blue eyes and light coloured hair, and belonged essen-
tially to the blonde type of Eurafrican peoples. It is also very
probable that there were also in the island from early times
people of darker complexion and hair. In the eastern islands of
the Canary archipelago early voyagers describe a race with dark
skins, dark hair and thick lips; some of these people doubtless of
African origin might have spread into Teneriffe and account for
some of the peculiar features of that country. '
In conclusion there appear to have been in Teneriffe,
(1) A dominant race, the Guanches, tall, blonde, blue-eyed,
muscular, with a skull of the first type.
(2) A race with a skull of type two, also tall and, as far as
evidence from their mummies go, probably blonde.
168 Mr Shrubsall, Crania from Teneriffe. [May 11,
(3) A Semitic race, with a skull of the third type, probably
dark and of medium height.
(4) A brachycephalic race (type IV) probably short and dark.
The records in European history anterior to the X Vth century
relating to the Canary islands are very scanty, but from them we
learn that the only races known to have been aware of the exist-
ence of that archipelago and thus to have come in contact with
and possibly had some influence on its population are the Greeks
and Phoenicians possibly, the Carthaginians certainly; the Mauri-
tanians who invaded the islands but were repulsed except at
Lanzarote and Furteventura; the Irish, whose missionaries under
St Brondan appear to have reached the ‘Fortunate Islands,’ and
finally the modern Europeans of whom one nationality, the Span-
iards, conquered the Archipelago. At the time of the conquest
the islands were certainly inhabited by mutually hostile tribes
differing however only slightly in physical features and speaking
similar languages, although on these last points there is a conflict
of evidence between the various chroniclers of the invasion, and
as the earliest accounts of these people agree in most respects
with those of the ‘conquistadores’ and also with later descriptions,
there can be no doubt that the islanders must have been left
undisturbed for a great number of years, perhaps of centuries,
uninfluenced by the great migrations which have shaken Europe
and rendered racial differentiation therein so difficult. Possibly
then the Guanches, or typical race of Teneriffe, may represent an
early race of mankind existing down to the present day in com-
parative purity under conditions similar to those which have
preserved the characteristic fauna of Australasia. Their physical
features lend support to such an hypothesis; for, on the one hand,
the Guanches resemble the Cromagnon race, more especially those
relics of it discovered at Solutré, and also the Basques of North-
western Spain, while, on the other hand, they have many features
in common with the Kabyles, Berbers, and Hamitic tribes gener-
ally of North Africa. The other and less dominant types in the
island have very probably been introduced at the time of the
various discoveries of the archipelago by the Mediterranean races.
1896.] Mr Shrubsall, Crania from Teneriffe. 169
TABLE OF SERIATIONS.
Length, Height, Index.
ae Teneriffe Gomera | heonanae
3 | 2 8 s
Aisle) ea/e& |/aje] 3) 4
63 1 ae
64 1 a
65 Oe || 1 3
66 a) 1 Oe ed
67 | | 4 4 1
68 )-23)| 4 2 3 1 AAT 5
2) eae | ime EY | 10 5
Re eeun eda. ee AO OP Sod! yall we
rise a |, We Ba iS. 199) 18
Bo hon |S) il) Bl Sse lees | 20m) 12
ie 3) | 3 "i Gale l4 | a7) 14
MA Uh | ce || 3) 4/3] 18 | 12
75 | 6 Ho 4 | i 94
7) 3) | 3 dene oe i gm) 14
os aeteet $e | 7 ay alas
er aber | i ete
02 1 hese |
80 ae | 1
|
170
Mr Shrubsall, Crania from Teneriffe. [May 11,
TABLE OF SERIATIONS.
Breadth, Height, Index.
Grand : Total
Canary Teneriffe Gomera. Archipelago
= 3 5 3 I = I 3 =I
5 = ey = = cy = cs
78 1 I
9
80 1 1
81 2 2
82 1 1
83
84 if 1
85
86 1 2 | 1 D, 3
87 1 1 4 ie 4
88 1 4 4 2 i | 6 6
89 1 6 2 1 1 | 8 4
90 il 1 3 3 2 ie Ale NZ 9
91 5 6 1 5 8 |
92 1 1 6 1 2 Wap ae, Ties
93 4 3 a 3 2 2 14 8
94 2 2 9 8 2 13 12
95 1 5 3 4 3 q 11
96 9 1 4 3 By 2 V5) 6
97 1 3 1 4 oy
98 2 2 5 1 1 1 8 4
99 3 4 2 1 1 8 3
100 3 1 1 4 2
101 6 1 2 8 2,
102 2 1 2 1
103 Hi 1 2,
104 1 y 3
105 1 1
106 1 1
107 1 1
108 1 1
Ne ee
Mr Shrubsall, Crania from Teneriffe. 171
1896.]
TABLE OF SERIATIONS.
Upper Facial Index of Broca.
a oe
°
ey SO[VULI FT 4+ Ae ANE OMMErNOS OHO AN 4 il
o
= = = = — = —
—
3
5 SolTBIL BAAN MD DOO O D 119 19 HO 69 OD 09 aa _
< a
s So[BULO eS Sqn NAAN
o
g = —— =
S)
S sr AAA AMANNG AA
2 SO[VUlI TT a UN SH MOAR ANAST AN cl a
: ——_ oe
cB) —— — =
5
al Sole SH SAIN OHAG AON AA -
il OA a ANAM =
Sb SOT BUI,
aes
ga
os
S sole AH OHONAT NAAN aa
ORORDOHNAGHODORDROAAMDHNOrRDHOAVAGDHGAOMrA
DIDDMOODSDSHSOSSOOOREREEEEEEErDDDDHDDHHDD
xopuy
172
Mr Shrubsall, Crania from Teneriffe.
TABLE OF SERIATIONS.
Orbital Index.
[May 11,
|
Gane | Teneriffe | Gomera Archipelago
& 3S @ S % 3 2 es
cue cer ch Pe eGo secs |S
1 i
1 1
1 1
1 2
3 3
2 2 1 4 iT
1 3 #
3 1 a 1 1 11 D)
1 1 3 4 1
1 1 3 1 1 5 9
AN) 2 7 1 2 ees
3 4 3 2 6 7
1 1 4 3 4 9 9 G
6 6 5 Di 8 7
6 4 5 l 1 11 6
2 1 2 2 2 1 6 4
2 11 3 5 7 15 13
1 1 2 1 3
3 5 8 12 4 3 16 22
tS} 1
1 i 1 2 1 D) 5
1 3 1 4 1
ee ad 2 | 6
2 1 3
1 1
1 3 1 3
1 1
Mr Shrubsall, Crania from Teneriffe. 173
1896.]
TABLE OF SERIATIONS.
Nasal Index.
So
a SoTBULAT OO AA AMDIDOOIDHNODOMOONAHAGN —
a3 g
= SO[RTL AGH OPM tHMDMORANHINMN NA Fe
< SS —
J So[ Bula, fo] Aes aH Neo — —_—
Sy
g =
S SORIA NAMA HOAN HON _
P| So[BUl9 TT ARAN HHO KN He OS OD NN —
5
[| a
8
iS SOR] nN ol MID NO DHOOM OM He AAO H _ a]
a So[VUla,T ANS AN Noo] ey ee ee
q4
a2 - ——
aS
o STB — NA SoH es HN HNO es] =
FDHOTANDHOOPrARDTOHNAMAMONRDADON
xopuy OD Of GO SH SH SH SH SH OH OSH SH OH SH 19 19 19 1091 19 191919 19 SO
13
WOOL, Lx. PT: Tit.
174
Mr Shrubsall, Crania from Teneriffe. [May 11,
TABLE OF SERIATIONS.
Facial Angle.
|
j a Total
ee ane Cal SORoe Archipelago
ca 2 ra % = 3 a R e
Sl a) 8 ley Ue Ba eae
& = es = es = ey = | &
68 1 Heed. 2 |
69 |
70 1 2. hla 2 2
ale eee | ilies teal
On eal eo Tat bia Mee et on la
Ce ed onl ee 5 |
(elo Pa Be) Bolle fo Bio. | 8
75 7 2 5 CAN 3 16 12
Go| Se Be Gi 2 cll wile lee lee
UG 3 3 4 MW 7 6 a al?
78 3 2 4 i 2 3 9 5
ao 1 2 2 1 4
80 2 3 rhe | 7
81 2 i | 3
82 Ibe il
83 1 2 | 1 2 2
84 1 | 1
85 1 1
1896.] Mr Shrubsall, Crania from Teneriffe. 175
TABLE OF SERIATIONS.
Height (by Manouvrier’s method).
Teneriffe. | | Teneriffe.
Bimcode A Sy :
cid Sails Weds ue Salted
eee Sindr fliers a chee
_ = Bie i a a
||
| 1460 1 |} 1620 |°13
| 1470 | || 1630 | 18
| 1480 WL WeaiG40 | |.23)
1490 1 | 1650 |.16 |
_ 1500 2 | 1660 | 19 1
| 1510 3 1670 | 9
1520 3 1680 4
1530 | 7 || 1690 3
1540 | 15 ee 10) |
1550 2 LO” fehl 2
1560 | 8 1720 |
1570 | 9 1730
1580 | 8 3 | 1740
1590 | 5 | 1750
1600 | 7 | 2 || 1760 |
1610 ke | | |
| |
138—2
LENGTH OF LonG BONES AND HEIGHT CALCULATED THEREFROM.
| Sex | Length | Height] Sex| Length | Height
| Mf. 425 | 1613 || M. d 1599
| M. 429 GO eee 315 1491
Sgrigs I. | M. 445 1648 || F. 329 1529
| M. 453 1660 || F. 342 1557
Sex Length Height | M. 437 1633 M. 360 1634
Femora
413-5 | 1584 || M. 373 1661
413 1583 Series LV. F. 339 1550
439 1636 M. 375 1664
417°5 | 1614 413 1536 || M. 381 1677
F.
412 1580 || m 440 1638 | M. 361 1636
422 1608 || F. 419 1546 || M. 363 1640
397 1496 | M. 414 1585 || M. 358 1630
4105 | 1576 | 425 1613 || ™. 372 1659
408 1527 || F. 400 1505 | M. 355 1624
406°5 | 1524 | F. 411 1532 || F. 343 1560
419-5 | 1604 | M. 437 1633 || M. 365 1644
425 1612 || ™. 441 1640 || M. 363 1640
BS EE BPP REFER BER SE
439 1636 429 1566 || M. 376 1666
447 1607 455 1662 || M. 369 1653
454 1661 | 462 1672 || M. 382 1679
| 434 1575 || M. 377 1668
Series II. 44] 1640 || F. 333 1538
453 1660 || M. 395 1624
459 1668 || M. 358 1630
427 1616 || M. 367 1648
412 1530 || M. 373 1661
44() 1638 || M. 366 1646
455 1663 || M. 374 1662
445 1648 || M. 369 1653
437 1633 || M. 363 1640
F. 413 1536 |
M. 42] 1606 |
M. 435 1629 |
M. 419 1602
F. 385 1462
M. AAAS) |) IL XSsI
M. 427 1615
Bei io Slee eS el elie is is ela is ler ba el ba ia &
M. 440 1638 431 1569 || M. 341 1595
M. 471-5 | 1693 418 1546 || M. 357°5 | 1629
F. 410 1530 443 1644
M. 416°5 | 1593 429 1566 Fibula
M. 418 1599 481 3
M. 429 1608 A Sea la 3
F, 413 1536 417 1582 || . 343
M. 426 1614 432 1624 M. 356
F. 409 1529 428 1617 || F. 339
F. 407 525 416 1593 || M. 352
M. 423 1609 496 | 1614 || m. 361
M. 490 1606 [hore 341
M. 436 1627 Tibia | M. 344°5
M. 417 1595 M. 345 |
F. 499 1552 M. 357 |
| M. 359 1632 || M. 359
Series ITI. | M. 368 1651 || m. 361
| F. 342 1557 || F. S28
M. 440 1638 || M. 375 1661 F. 327
F. 418 | 1544 | M. 360 1634 | M. 345
| |
May 11, 1896.] Mr Shrubsall, Crania from Teneriffe. a
LENGTH oF Lona BoNnES AND HEIGHT OF LIVING CALCULATED
THEREFROM.
| Sex | Length Height| Sex | Length | Height
pas lw. | 328 | 1652 || v.| 307 | 1566
: M. 316 1619 || F 297 1542
Sex | Length | Height |) M. a2at 4/4637" | ¥. 302 1555
M. 322 =| 1634 | . 325 1644 || M. Hill 1605
1b |
F
F
mm | 331 1659 | mw. | 329 | 1655 997-5 | 1546
m | 327 1648) |u| 33 1659 282 1513
m. | 310 | 1600 || w. | 340 1675 ; 298 1547
mee 299 «=| «1546 || uw. | 332 @«6| 1662 || w. | 329 1666
F. 288 1512 | a | 328 1652
F. | 298 1548 || x. 305 1564
mM. | 325 1643 | F. 319 | 1600 Radius
m. | 316 LOLS wa ele oon GED =
F, 319 1601 || M. 333 1664
Wares, | esd | Je sar | roan || | O22) | ee
m. | 324 | 1640 | w | 299 |-1546 || | gas | 1660
r. | 306 | 1564 | w.| 319 | 1626 a nee er RReed
me s09 8 11570 |r. | 323 | 1612 |)" 7
F. | 281 1480 || m. | 329 1655 ||
Meet Polo 1616 || M. 331 1659 Ulna
F. 298 1511 || Mm. 338 1677 ||
F. 303 1556 || M. 326 = |_:1646 ||
M. 315 1616 | . 317 1621 || M. 274 1710
M. 306 1584 || F. 314 1583 || M. 268 1677
M 322 1634 || M. 330 1657 || M. 270°5 | 1694
F 307 1567 || F. 306 1564 | M. 265 1669
M 331 1659 | F. 309 1570 | M. 267 1674
F. 296 1538 | M. 318 | 1624 || M. 256 1638
F.
M
M
302. | 1554 | Mm. 324 | 1640 || F. 231 1542
307 =| 1585 | Mm. 315 1616 || F. 243 1583
314 1614 | F. 298 1541 || F. 255 | 1645
Recent literature on the physical anthropology of Teneriffe.
Verneau. Rapport sur une mission scientifique dans l’archipel
Canarien. Archives des Missions Scientifiques et Littéraires, Vol. x1.
Paris, 1889.
Verneau. Pluralité des races dans l Archipel Canarien.
i> Bull. See. d Anth. 1. 3. 1878.
2. Bull. Soc. dAnth. 1881.
Lajard. La Race Ibére. Bull. Soc. d’Anth. 1892.
Lobau, Die Insel Tenerifa. 1896. With complete bibliography.
Chil, Estudios historicos, climatologicos y. patologicos de las Islas
Canarias. Por Dr Gregorio Chil y Naranjo.
Sabin Berthelot. Antiquités Canariennes. Paris.
Sabin Berthelot. Mémoire sur les Guanches. Mém. Soc. Ethno-
logique, 1. 1841, p. 129; 11. 1845, p. 77.
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Barnard Davis Collection
494 503 505 508 510
a TN
—
43
195
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136
129
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374
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566 567 568
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5694 570
571
MEASUREMENTS IN MILLIMETRES OF MALE SKULLS.
Number... 1 2 3 4 5 6 7 8 9 10 at ay TB} GS aS Wak) SG) EN) EPR) OBS et
F arab . Cambridge University Museum Private Collections, * ae Vantin ya Basel Bie tee oe Se e grog ey Ce Belo ee 460 47 «48 49
useum. Catalogue Number = $0 FG PS GOR ups Sant Cx Hemeretite M15 mIS m20 M21 m22 m23” m25 m26 m27 m29 m3z0 rivato Colleotion at Orotava | Barnard Davis Collection Royal Cotte oreo ae
i 20 re . ¢ ~ e » s
Maximum Length. — 174 189 188 177°5 191 181 173°5 179 182 1176 188 178 180 174 189°5 183 180 179 180 189 184 187 182 195 — 476 189 181 190 186 ~ - pa 593 $05 S08 510 566 567 568 569 560, 570 571 573
Maximum Breadth . — 135 137 139 138 — 140 148 135 142 138 144 134 139 135 144 142 137 132 140'5 143 140 145 143 146 — 136 143 137° = ee ete 182 — 169'5 179 183 182 177 179 185] 183 195 191 181 18 182 7 - ‘i
Basi-Bregmatie Heigh — 120 — 1395 128 — 137 130 126 128 28 135 124 127 121 132 134 133 127 136 134 138 132 128 — — far tar a ae ey oa 144 — 129 140 138 134 138 132 136} 139 146 136 140 193 138 193 T94 187 192 187 18r 182
Minimum Frontal Breadth 94 89 94 95 925 96 100 96 95 99 |95 89 96 94 97 98 96 92 92 955 96 93 99 98 97:5 — 96 101 a 35 128 136 128 130 12I'5 130 134 130 127 138] 127 130 129 137 137 14 143 140139 145 146 140. 137
Bi-Stephanic Breadth . 10§ 110 105 113 121 125 99 is = 95 875 98 88 81r 90 86 94 96 88 o4 92 98 103 92 98 37 140 I4O 140 133 128 134 131 130
Pterion Breadth ... — TOF SUG TOY OeHy Tots FO Tere) — = Sa = = 121 114 100 a 93 To2 105 104 98 99 99 91 Oy
Asterion Breadth .... = jo = WG ie WE HO We _ = = 113 120 — aS ae a 123 124 108 127 106 111 108
Sub-Cerebral Zin 129) 27) 31) 18) 116) 21) 20 = =i = 108 106 114°5 07 ee ao 1o7 12 107 113 107 110 108
Total Frontal — 116 125 124 117 131 130 129 130 112 I2 115 — — — 122 121 118 121 130 = <p = 24 21 26 26 oi SS HO M9 M0 116 110 104 106
Parietal . — 112 130? 134 107 139 135 — 112 130 II5 129 13I 129 112 131 147 = 113, 123 123, 132 21 142} 120 123 128 130 = rae ap 2 27) 7108 a8) a3 laa
Supra-Oceip: — 6 — 73 78 — 67 72 = = 118 WIT 123 135 131 140$ 114 198 11 128 = ar 132 137 132 126 126 122 120
Gunes Total Occipital — mo 1132? 118 — — 110 109 115 118 WII 122 — — — air 118 125 I10 103 = = = SN) 8) ok Bom = Oa 130 He 132139 120 122 126
Total Sagittal... — 338 371 376 — — 375 — 357 360 338 366 — — — 374 368 355 362 380 ae 119 128 126 113 110 108} 121 122 135 109 - Be “ae 2a 19) 077 8a S879
Supra-Auricular — 281 295 295 290 — 306 297 280 288 Ago 291 300 303 299 292 310 ee 350 372 372 347 362 390] 355 383 374 367 365 ma pet 13S" TIO) 135) Lag) 1107) srry
Total Transverse = 409 — 472 430 — 451 444 = 285 294 298 312 292 300] 309 — 305 311 302 303 37 395 380 390 368 351 361
Pre-Auricular ..... — 255 245 225 230 — 234 233 > = 435 418 ro) oe 33 312 320 302 323 305 303 302
Total Horizontal — 493 515 512 501 — 509 498 516 524 510 530 — — — 515 516 507 468 == 253 245 SS 246 455 AOI 27 451 449 430 428
Foramen Magnum Length ... 35 38 (O Bo Gs O23 (ho “A By BS sy? YO aa aa oS7 = = = =: 507 516 503 515 468 530] 598 — — sto 4g9 516 oe ae Bae 241 221 226 220
Foramen Magnum Breadth 31 30 34.32 «32 «30 |28 27 28 33 31 33:5 31 34 27 a = sae SUi3) TAOS 53359 932)) 37/0092 bas) mons STONES MEG TT ah 2 33 ses a “ 503
Basi-Nasal Length . — 95 — 105 101 — 96 96 100 95 102 105 102 95 93 1015 100 104 92 95'5 9 iyo, es a i go 32° 31 29) 427 30} 30, 34 32° gn i290) |a] bam an Role S37 3737
Basi-Alveolar Length — 90 — 100 99 — 92 89 92 89 |95 100 98 91 89 94 92 985 83 ae w % 875 a = of 35 ca aa x06) a 2 9r 91 95 98 98 96 92 103 101'5 Tor Tor 160, an a oh 5 88 30 313031
External Bi-Orbital Brea Tor 98 104 115 105 102 109 108 = & 94 go 87 895 101 95 — 83 95] 99 or 90 of 94 03 08 o7 < D 102 99 102 104
Internal Bi-Orbital Breadth 92 93 97 105 97°5 96 100 101 1 = = = = 10S 105 103 107 102 11t II rie 108 ot or MELO
Bi-Jugal Breadth ......... 108 106 116 123'5 117 105 115 121 125 — 120 122 123 121 126 i. = — — =] 101 97 98 99 oyunoaetos 18 ae oH aa 33 a
Bi-Zygomatic Breadth — 125 127 134 134 — — 143 135 — 130 130 136 132 129 139 126 131 126 1 129 I 3 6) = 2 2 = —} 11355 — — 113 108 8 ar ab
Bi-Maxillary Breadth 99 91 93 Il0 Yor — 102 08 = E 110. OI a7 gr 38 36 36 fe iD B 95 aes za 233 om “ ae rH = 20 117'5 1330 — — 126 134 a _ aS 122 ar a rc a ng mw peat
Bi-Malar Breadth ...... 112 107 116 124 119 112 2 yj 9 4 94 95 95 99 85 — oF 102] 1043 — — 94 91 99 G0 Ios Tor a 37 29. 129
Ophryo-Alyeolar Height 80 90 95 101 82 80 84 80 —}| 116 — — wo 107 119 11a Wi8 113 118 ae ae oh
Naso-Alveolar Height ... 59 65 68 72 66 62 64 59 62 71 67 68 64 67 66 65 B om OF CH Oo «6 65 Go. EF. " = go 86 84 92 S88 8 6 8s 8 S:
Spino-Alveolar Height 15 22 20 21 15 142 17 I5 17 24 16 21 15 13 20 14°5 15 20 13 21 ie % 3 ee 7 we a S7 64 88 87 35 8 38 fo 58 68 65 — 61 70} 69 65 62 68 58 65 nH 7 64 “ a e a
Orbital Breadth... 38 37 37 41 40 39 39 40 35 35 9 41 37 36 35 41 40° 37 40 40. 38 gs 35 41 ay MAGMMASINMO 36) gi qa 8 4 99) 40) 4s) ae) Ghee ace cel) LS SOs Ran ao ao ats s eo ea ae
Orbital Height . BL 29) 32) 30: 33 29 33-30) (27) BO) 33° 30) 20 28 31 432 32) 32° 35) 34) 28) 30) 34m s5peesdmmen m0 33) 358261 32 3 oe aS Ag 30 40 38 39 37 40° 37 37 37 40' 4a 39 “do 4g) 38) a8
Nasal Height. 44 49 52 50 49 47 45 46 48 52 48 50 55 47 51 50 Sr 52 46 49 53 45 53 555 SI'S a7 51 48 48 49 43 46 SES 2 030) 130 ay 1920092 ]/ 132) 134 p32) 32) 3015 gah cc cOmed Sa
Nasal Breadth . 23) (24. 22) 23-26 «23, «24° (23) 25) 125) 2015) 26) 28) 22) 23:5\ 21 “2275) 23) (25) (25:5) 23! 25) 22) 27 enmeezme2S) 22) 20'5) 122) 26/8 21 Be ah a7 pox st = 2 2 50 48 49 41 47 55 52 45 56 St 47 B
Bi-Dacrye Breadth ... 22, 24 23'5 23 20 23 23 24 26 (25 25) 22 25 23, 25 21 24 23 24 23/ 22 24 25 245) 24N2AccN 27, 26 (25) 22 2 2 25 1 23 2 5 ce - Pky EINE PXY ey FY - 2 a2 2 25 2 2 2 2, ar
Pxternal Palatine Length 2 58 55 54 — 53 48 G) G3 Gy 76 Go Ge 7h Ga Ho Sis 2e 123 7 ee 20 A 3° Fs 20 20 — 25 27'5 25 21 a5 320 92° 30 a0
Internal Palatine Length 46 55 47 — — 48 44 St 52 47 50 52 45 SO 52 46 54 40 42 2 nal & f f \ 52) 55 49 52) 49 Sr 51 50 45 56 ‘0
External Palatine Breadth .. 57 G6 665 62 — 04 56 ms Sano nee th es ae eS SF SoS) 9 AP ich a han erRmr Ss ask Maen cnt: ee ee 68 oo i AM i
Internal Palatine Breadth .. w wy p= = F a Gi (2 2 20 Mm gH eB gy) sh co 2 8 to) 6 2 2 — a ee 2 59 56:5 Or s4 O61 60 68 60 68 65 — 4
3 3 Bs 4! 4 4 35 36 40) 42, “41, 935) 35) <4 37) 140) 40) 932) — 2 46 35 32 31 EE SEN RYO Co ky cK} 38 30 9
INDICES.
Length-Breadth we — 776 72'4 74-7777 ~ — ~—«'77°3 85°3.-75°9 78 76'4 766 75°3 772 776 76 77°3 761 73°7 78 75°6 76" a VAS 6 — I : 6 75" : ‘ . . . D 3 , . ? 2
Length-Height = TES 74 TA TET TRS akg Jo8 703 127 719 097 Jo6 60's 698 752 139 709 756 709 78 Joe Jon ~ — fog fet © deo yg Be Fee — Foy ope Sat 36 7m om Tae Gon GOS cae Fue 2a 188 an 1s3 Tes Tas Ta 77a) 183
Brendes ae — 88'9 — 103'6 92°38 — 97°9 87°8 93°3 901 92°8 93°7 92°5 91°4 89°6 91°7 94°4 97°1 96'2 96'8 93°7 98°6 91 89'5 — — 96:3 986 — 938 of fb Le = RS 88 an qa es hee a hi Re aie tee a ais rae api my a ns
Upper Facial (Kollmann) — 52 538 53°7 493 — — 413 459 — 51°5 52°3 471 S0°8 S12 4677 50 514 '2 51°9 50°7 53°1 582 47°8 — 52:4 41'6 48:1 52°3 52'S 40'S 414 — on een Se ere an te 9 103, 1014 97'9 95'0 9517. 88:4 O1'8! 93/0 949
ao aaeiill (Brood) je = WAG eh Ge a6 SOReS: 53 49°2 $§1°9 50°7 53°1 58°2 47 52°4 416 481 52°3 52°8 49'S 41-4 50 49"4 52°33 — — 484 52'2 _ — ars 49/6 Fes ae Ae 59°8 sor fort ct
Orbital 85°7 83°8 78'4 78 75 84°6 74°4 82'5 85°7 771 83'3 80°5 81:1 806 80 75°6 77°5 86°5 80 87°5 89°5 80 85°7 82°9 83°7 79 842 77'5 79°5 80'5 83:3 684 78 74°4 77° We 8a) Ll ROB ad Ba. Gig) |Boy BER GRE REC ree URE GRICa Ee ean Ste
Nasal ..... SII 523 49 42°3 46 5311 48:9 53°3 SO S21 481 55:2 52 50°9 46°8 46°7 42 441 44°2 54°3 52°1 43°4 55°60 41°5 48% 44°6 408 54°9 158 552 48-9 60°4 467 ar He a0 gon 4a = 142 14 12 ta sat ue oe ion He He Lae LE LER US Eh
Palatal (Vitchow) S42 674 67's O81 — 792 818 G08 S08 723 84 846 734 76 712 704 741 $0 go's 75 89 88:5 777 953 O86 G2 — 784 84 837 729 70 788 So4 9019 784 O27 — “No 93, O86 Tha O43. 8a OPN tad. Coad Gee CEVA Cle
: (Flower aes oat 2 0 = . “ . 6 . 5 d A a . . A i . seca . t is - 7 . é ‘ x i Sir ciacece # 19 3 z i 0
ANcoley (een = Cel = oP ae =e 958 eee, 92 93°7 931 95°2 961 95°8 95°7 92°6 92 94°7 90°2 92° 92°8 90°6 96°1 90°5 93:9 — — 95:2 88:7 90:7 907 98'9 916 94'2 103" 96'9 90/a(92'4' (98 0; Bort) (Or. 190ld 310.0 Aino 7G oie Osama Org of
Supra-Auricular—Total Transverse .........— 63°7 — _ 62°5 674 — 67'8 66°9 = — = ay, Dee ee om a ths aod 20 1 ye Ha rae) 20/5 oa 1819 ie
Pre-Auvicular—Total Horizontal . — 51°7 47:6 43°9 459 — 46 46°8 — eS S = = a a ag Got We eats 6G o9'4 feed pay 67'9 70 (hen
Frontal—Total Sagittal .. D343) 3357, 33) =) — 3407) = 330 air g3;n gua — — — 32:6) 32:9) 33:20 33'4: 34:2 = = PET AEG OMELET COM CeCe ercpcon ATT ATO EE ABT da aa SE
on tn Total Sacrittal 2 Sete, a OU PEE COE ee ea 9 33:2 334 34° Ste 32°3 33° 331 38 33% 364 33'S 321 34'2 35'4 344 351 34°7 34°7 32'1 34'2 ga’ 33'2
Parietal giotel Sagit 331 35 35" 36 314 361 34 35°2 35 33°3 315 30:2 387 = = 5 30°9 29'S 33°1 38'9 30°2 35°9 321 36 2017 349 33'3 340 30% 34°7 35° 32° 34'8 349
Oceipital—Total Sagittal... 32'5 30°5 31°4 — — 29:3 — 32:2 32:8 328 3399 — — 29°7 32:1 35°2 3074 27°1 — 34 34°5 30°6 32°06 30% 27'7 34'1 31°9 36'1 29°7 32°2 30°3 34°9 30'S 32°1 33'2 30'5 319
7
8
Private Collections at
174
136
122
96
9
179
138
130
95
sence
LO ee 19 30 «31
ollection
ae 506
es
Ti 7ee oe aa Ly) Lr
139) TAOhs Papers 79 nee
Tage 127001 T2912
96 95 1 95 88
- — 108 109
_- — 104 108
_- — IOI 102
—_- — 18 18
128 115 ToT err
120 116 II4 108
SS 76 89
II0 140 120) 122
358 365 355 341
292 298 -—D 296 291
— — -8 404 401
SS 200210
500 505 + 517 487
37) 34h = gOre 36
30 325 — 29 30
91 915 9 98 96
86)787°55 5 93) 88
— — -+3 Io1r 98
mn a 94 92
114 — 10g 104
122 116 142 119 —
— 83 102 89
—- — a 108 102
—- — a 86 85
65) 57 69 ~=«66
Tom 4 A) LO 7
Bo 38. de 38) 637
Gh 30K A. 3328-82
SRD) Bey 22)! .2R
48 445 4 50 50
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51 46 4 47 46
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41 35 4 so) ae
|
81°377°3 73 77°4 772
77°8 70'2 72°9 7371
95°7 90°7 98 94'2 94°7
533 491 49 58 —
— — =a 72°3 —d
88°6 81 8d 84'2 86°5
45°8 44°9 7 42 40
80°4 761 8 83 67°4
94°5 95° 94 94°9 91°7
—- — 14°9 16°2
= = 3 73°3 72°6
= SS 39°83 4371
35°58 31 34°1 32°6
S510 othe 32:0 387
3025 S07 33°8 35°8
36
514
37
38
39
!
Royal Coll. of Surg. -
572 5734 5738
eS
180
144
127
Number... 1 2 3 4 5 6 q 8 9 MO) ah = py ey ae oS Gi? ST) ON) Oo RH 2 30. 31 82° 88 (84-36 86 <87> Sona
MEASUREMENTS IN MILLIMETRES OF FEMALE SKULLS. |
Museum. Catalogue Number x pane dge University Museum Private Collections at Basel, Santa Cruz and Orotava Barnard Davis Collection Royal Coll. of Surg.
a eee ee 2 53 84 85 — 1716 mig m24 m28 493 495 496 497 498 499 500 501 502 504 506 509 SIE 512 513 514 572 5734 573B |
Maximum Benet ec Gres I 8 Fomaen 2» on Ee GS SS »
Maximum Breadth 7 19 175 171 183 181 164 188 174 179 171 181 182° 174 169 189 173°5 175 18375 185 188 177 178 182\ 172 183 172 163 180 170 177 171 175 -170 169 I8t 189 170 180 179
Basi-Bregmatic Hn 138 140 138 137 143 132 143 136 138 139 140 137 134 135 igh) 34 == == ko) IO) TEA TG) Te 136 146 140 14% 143 136 137 132 140 131 140 134 143 132 144 44
Minimum Frontal Breadi, 130 118 124 130 124 131 123 122 130 133 127 135 133 125 133 125 125 126 134 132 124 125 129 124 117 128 125 133 — 129 125 122 123 127 126 129 122 127 124
ares Se Sa 95'5 865 86 92 96 92 98 06 95 96 95 I00 93 89 107 92 96 IoI's 98 98 86 1 99 99 94 94 90 96 94 95 88 90 oF 27°80) 07 Oss no2maron
104 III III 119 108 Ti SIV OL) TD | WEE DWN) WG) HES OL) ae ORE te GIN my Hoy) ini 119
SS ES ee UNOS UCYL TNO. TR fie) OH |i) =. => sa oe — — — 112 108 I00 try 103 IIL 104 102 112 ro$ 104 108 105 103 109 104 112 YO4 109 I10
Asterion FS Siaisiniwivjureieiwiutncaieinie’elsis|sicinjeicie c/eie 106 102 100 108 IIo ee 120s = — oe a = ==, — — — 108 108 105 ee 104 99 IIt 106 106 ae To2 oa 102 100 103°5 110 to8 1 13 103 IO {OS
BUCFEDT A Reece eae A) On BD 225. Gea eee Ss ee ee WS 23 BB I Tea 1S) 0729522) 722 ear 19 2
Total Frontal i Bl Bik IG) |) pe} ie) 22 Bi FO) De 5) 223 i 7 Z QO)” 19) eb
— — 125 115 121 129 132 122 121 317 132 !I9 21 122 128 120 115 12t II 115 114 122 111 128 121 123 120
oe eee ee 127 120 125 127 121 114 120 114 127 128 115
I2l 122 123 122 132 124 123 134 122 125 115 114 109 124 13% 114 108 130 110 315 125 122 for Tar 137
SSSCoo Sao see SoUSH OBE OOS HOEOSEG 126 115 Il 110 122 129 112 100 126 120 116
Parietal =
Resear taemerenecen ics J 3 83 OR SA” Cs
Supra Occipital SA apc an ee SE 61 65 «(71 75 6 — 73 68 o1 76 89 70 66 70 66 80 8 65 (69
Curves zoe Occipital SOD SA ea NBO COS SHON CSED 116 126 122 131 120 107 121 131 116 110 140 — 132 110 III] 12% 124 130 116 — 111 114 126 109 108 127 — 120 122 110 114 107 I17 120 122 105 III
SSE ES FAN goers aed 367 361 366 366 363 350 69 358 36 — 378 — 372 388 376 360 — 365358 362 345 345 371 — 355 341 355 338 344 353 373 344 352 368
3 35° 353 345 369 358 365 379 347 372 3 379 3 365 3 5 <8 ;
Supra-Aurieular... o..0......cccss00:, 282 292 296 302 248 293 288 275 282 292 208 298 285 — — 292 288 281 296 315 | 303 299 294 290 305 260 296 291 291 288 308 287 jor 286 310 302
Total Transverse ........0..cc..00.., OS mOmE—areanroy ara passe = — — — 440 438 gor 420 431 413 413 411 419 434 398 404 401 406 410 422 405 428 396 430 425
Pre-Auricular ssc = 2 ==), eee Se np Se 2 | 216 222 219 209 211 210 206 210 226 228 231 206 240 21 5 231 240
= ia 09 193 221 224 262 210 268 264 260 227 210 23 ASN VGH FON GS) Gal Gi? Rn ies fan oP 500 326 46a Crate
o OLZOn tale eee eee Be) Bjos) ey riy Gis} ass) lo) kos) Lfote) [yfofo) fof) ee Lol ne 512 525 490 510 § 4 2
Foramen Magnum Length ........................ SEE MC OMICS ESS IEESGHINGSIgng5. 36. 937° 41 —=- = ==, 3% 36-34 34 gg as gg 33 37 36 36 sola 8 36 34 33 34 36 36 33 36 2
Foramen Magnum Breadth..................0..... 39 JO Bf 35 BO BRS) BY As 3 go spy Sa Ps) I) OSsCéo) ss 3 Se oh aes 3 ae a8 ar 2 a : 3 5 3 d
nce Nasal lyon ehh. ons ee ah ae OI 90° 8996 98 95') 08 06 OF Of O15 91 93 94 102 96 100 99 98 100 91 08? x 3 ae 2 23 ae 38 26 2 34 : 88 oa ae
ins-Aevemlan mien wil ties ocean ca cnsicsse shea RO nO OME OME OO on ESS uerSS SO) S775) (87 (89) 84 93) 88) == On = = 85 82? + 76 5 7 5: 92s ee 98 10h. eee es Ey 93 ‘OC
External Bi-Orbital Breadth ..................... OR} TO I WO WLS i OS yy 2 101 102 — 104 98 Jor 98 96 98 98 o4, Tox ~O7 ToAearaG
Internal Bi-Orbital Breadth ..................... J OG G8 OF O88 O35 GS — = Se SS] SSS] By Os SS 88 93 95 — 94 95 94 92 90 — 92 98 95 88 94 99
CEES Pr TSS Les See ee cee ran PE2 013) 107, lO) UIs) 105 |ai5 123 112 114 — — — — -— — — — fir yr 107 — xr, — 105 112 — lo Tor 109) 1045) S07 s t4y One nLOmeanie
= 3 — 126 121 — 124 — 119 — 124 — 125 128 127 120 124 125
Bi-Zygomatic Breadth ... -.............c.ececeee ces 12 //a5 0G L222 ORL OM 2 Il 2 ome 2 5 l22 eeTTONeI2 5 ell2 settOsr32\e027.50—— | eT oOmT 2 7a 23 seeIITA GT 4 4
Bi-Maxi Breadth CueCOMOS MESO mE umneS sue eer = 85 gon 88 = 66 99) — 88 == == son Sn. 80 87 89 99 87 102 89 — — 92 98) o4) (= scomemag
i-Maxillary Breadth ..........--.:.sseseeseeceeeee 9 iB 2 OS Se ee ee eee ; Se 100 10s 107. — 110, 10] 108 oz = = prt uaa god
We ate POAC Gere oon cc aot. oc etesaeanabaeeneae 106 113 107 104 103 103 107 IOI 108 105 9 6 828 ; Zo 63 86 8s 72 — (80 88) equ GhmRummnN
Ophryo-Alveolar Height ................:scceee ee a Ce ee ee Blo o> AE aA = Bees 63 5? 69 66 59. —2 69) css cane mneemmmne
Naso-Alveolar Height ................:::seeseeeeee CORSON mn Sian 2 O70 025 05) 57, (61 (G0\ 952-62) 63° 65, Gen | 17 i2 16 I§ “15 16 19 «7 Iq — cs 39 one are umCeete
Spino-Alveolar Height.................2:sesseseeees ner; 2] 2) 1B WH IW Why Bo wey mw wh we iy TP NG 1} —5 Ao Ae) i} OR ie 7 34 36 «36 36 3d 38 gp as ge gt
TSE isn 0 She eee BO MOMNEG MS noes ES SS 9308 85 35 «37 35 «9 36) «4D «40. — «391-37 86 6) 33 Sis nee 2 32 27 32 32 3 — 34 32 92 34
PLS Sen eee Om ees ee OS 2GOMPES4ueS Tg GO 31) 30 33°32 «29° «32, «340 gr 31 328 gomeaT ate ae amen ee te ais ra.
Bi Dac Pee ee D2, Bil —«*I0)-— PB HS BN) OD YO) BO fo) PRE PAY A DWH) eon G 45 8 ai 50 a e — 47 50° 40 47 ees Oma
a oe Tee eee SA 7 Te 5 ATe Ay 6481 4455\ a2 48°39 «50 fo —= 149 48 Fol Age 43 ae Be i at 23 2d. ai Bo, aa age
Nasal Beek i eee 23 25 +24 22 22 22 23 24 23 22 20 25 25°5 22 i 20 5 24 24 Pee roe o aie 56 48 48 44 52 Sx — — 9 48) er Scola nen ce
Nas ee ee - 3 meet ae ea ae : t =
imteraalPalating engi, occu go G0 2 4 St 8 as SO Kw wo HH - Re “eS Be HE eB He 3 - Be Be Be
POL ATSIC) gonnhadaenbe tenon eeesoan a [2+ So ee 2 Rane Cae = ome — 6 30 30 6emEg2
External Palatine Breadth .................. 63 64 57 57 45 ee ee ra ee me me ae 32 34 «31.=«i«36:'—«ig2t:s«2]tsi‘«<StsCSCsCOD 31 3
i TUT Th aa eo ae Gleaec a2 ens een 4Omers7 35) 40 35 40 30 38 932 3 3 3
Internal Palatine Breadth ...............++ 3 8 |
EI DEIESD &. $ 81°4 86°5 79'4 80 2 80 771 828 74 75°7 776 80 8o'4
78 786 807 74°8 79 80'5 761 78:2 77 81°3 77°3 75°1 76°9 80'r 71°9 821 — — 75°7 74°4 74°6 787 78 releks ae: oe te a EE ER cs cyt bbe 2e 8 vo6 Gee
Length-Breadth ............---+- eee sneer as 6 66°3 72°5 71 68°5 79°9 65°4 70°I 72°6 77°3 70°2 75 77°3 74°9 70°4 72°3 71°4 68°9 72°4 702 7O1 70'2 70 oor ee ae a ee ee are ota tery een in rr
Length-Height Lo Ssttisss HO DAAQUMOOINDONO SOOIEONS ONG dee 84:2 89°83 94°9 86°7 99°2 86 89°7 94°2 95°7 90°7 98°5 99°2 92°6 97'8 SF = == ORY ORF 93'9 89°3 90) J Cnn She aoe 50 §3°1 2 5o'8 54 464
Breadth-Height..........-.:-sesceeeeneeeeeserenen ees re ete le ie ee AS 433) fort 4010 451 4g;7, 47 494 = - 45°5 48-2 53° = ie Obes | eg ee = ba eee
Upper Facial (Kollmann) .....-.---+--srrre F Oh = OS® Gare BIB GIG ST] OD) ONL AT} 82 ‘a 889 88°9 77°1 84'2 86°5 886 — 971 84°2 86°5 100 89:2 83
PPE dal (BOCA) .....2--2creee-eeeseecseontee® 64°8 664 5 3 : : : = 83°8 88:9 8 . vel 4 95°0 94°4 9 9 :
Upper Facial (Broca) SE eciace eriineinitiae ep 85 83°8 Sir 86°5 81'1 89°5 816 83°3 88°6 81 89°2 91°4 80°5 78 85 79'°5 83 9 83°3 93'°9 79 5 50 §2°3 41°3 46°7 47°9 483 42 AG. mig 489 46 45°7 42°60 44 5
Orbital eee eer aneemamntiensinr ne), pie "2 57'T 48°9 46'8 53°7 51'1 51'I 48'I 45'8 44°9 59°5 59°2 56°4 50 52 — 4 50 48 512 44:2 33°5) > yon 87°8 92"7 A 83 67"4 3s 7 — 72" 80 66°7 76°9 81:8 68'1
arsah eee owen nai sinamionrareisialaCe/eisis}72i8:0)2 oe 3 he 614 74°5 33-3 889 74 761 80°4 76°1 86:9 73°4 82°6 69°6 74°4 — 64 73° 77°3 83°3 69°8 646 ; Bee aie s : 96 : :
Palatal (Virchow) J ee aasonO2 Pe 50 907s INOIODIGUIOO IED ue Reo 96° 91°77 — ~~! — 917 96°7 94°5 95 6 95°6 95°7 89°4 912 91°77 — 96 Se = 934 83 7 : : : 5
Alveolar (Flower) ...-.---.---s1s-nns ey Ae ces 68) 1655 174 167 (Caras Se ees 661 OER
neat Tae Soa eae cei 2 — 1] BP ree eget eS ae, ahem 44
ep Me ee atalle ssc 4i't 38°9 44°6 43°8 50°6 43°5 S19 : ; ee Wek svi eye: Gil eee seit Le ae
Pre-Auricular—Total Horizontal ..... 6 33°3 34:2 34°7 33°3 32° 34 33 344 35°8 31 331 33 34 347 3
sen ee se RG BS ee eS
Parietal—Total Sagittal .........-.- 0" 343 39 333 35° 33% 30° 342 38 314
Occipital—Total Sagittal Se ndenceeqorgee
1896.] Mr Newall, On the Spectroscope, etc. 179
Monpay, 25 May, 1896.
PrRoFEssor J. J. THOMSON, PRESIDENT, IN THE CHAIR.
At a Meeting held at the Observatory the following com-
munications were made:
(1) On the spectroscope used in connexion with the 25-inch
refractor. By H. F. Newatt, M.A., Trinity College.
Mr Newall exhibited the spectroscope and shéwed some of the
photographs of stellar spectra with terrestrial comparison spectra
taken with the instrument. A general description of the spectro-
scope has been published in the Monthly Notices of the Royal
Astronomical Society, 1896, vol. LVI. p. 98.
(2) On a suggestion for a form of spectroheliograph. By
H. F, Newat., M.A., Trinity College.
The results obtained by Mr Hale in photographing the sun’s
dise with the light of some definite wave-length emitted by it are
so full of interest and of promise of further development that it
seems pardonable to make an untried suggestion which may lead
to increased facility in taking such photographs.
In a paper entitled “The Spectroheliograph” (Astronomy and
Astrophysics, 1893, p. 241) Mr Hale has given a résumé of the
earlier attempts to photograph prominences and of his own work
in developing the spectroheliograph. (See also Astronomy and
Astrophysics, 1892, pp. 407, 603.)
M. Deslandres has in a paper entitled “ Appareils enregistreurs
de latmosphére solaire” (L’Astronomie, June 1894), considered
various forms of apparatus for researches similar to those carried
out by himself and by Mr Hale. (See also Bulletin astronomique de
lV Observatoire de Paris, Feb. 1894).
The general principle of the method is as follows:
An image of the sun is produced and allowed to fall on a slit ;
the illuminated part of the slit is a chord of the sun’s dise. If the
proper relative motion of the slit and the sun’s image is brought
about, the slit can be illuminated successively by parallel chords
of the sun’s disc.
The slit is connected with some spectroscopic (or rather spectro-
genic) apparatus which produces a monochromatic image of the
slit, and this image is isolated from the neighbouring images by
180 Mr Newall, On a suggestion [May 25,
letting it fall on a second slit. We can thus produce monochro-
matic images of successive parallel chords of the sun’s dise.
Photographic apparatus is then arranged so that the mono-
chromatic images are laid side by side, and a complete photograph
of the sun’s dise can thus be reconstructed.
It is clear that there are many ways of bringing about the
proper relative motions of the slits, the image of the sun and the
photographic plate, but practical experience points to the desira-
bility of reducing as far as possible the number of parts between
which there is relative motion.
Mr Hale has in the case of the spectroheliograph of the
Kenwood Observatory attached a spectrogenic apparatus, con-
sisting of collimator, diffraction grating and camera, to an equa-
torial; and by driving the equatorial at the proper rate he keeps
the sun’s image stationary relative to the spectrogenic apparatus,
the whole being moved relatively to the earth. Then he moves
the slit relatively to the collimator, and the second shit relatively
to the camera, in which is a fixed photographic plate; the two
slits move at different rates but are connected by carefully designed
link-work.
M. Deslandres has used a heliostat, which does away with the
motion of the sun’s image relatively to the earth; and he advocates
the relative fixity of slits and spectrogenic apparatus.
Mr Hale, in using on Mount Etna a spectroheliograph designed
by him for the late Mr Cowper Ranyard (Astronomy and Astro-
physics, 1894, p. 662), made an advance in arranging that the
camera and collimator should be parallel, so that the image of the
sun and the photographic plate should be in parallel planes. ‘This
method has been adopted by Mr Hale for the spectroheliograph
designed for use in connection with the 40-inch Yerkes equatorial.
The slits and the spectrogenic apparatus are relatively fixed, and
the whole arrangement is bodily moved relatively to the sun’s
image and the photographic plate.
In this arrangement the resulting disc of the sun is round and
undistorted, and there is no need for the rectification of the
distortion which Mr Hale has had to deal with in his earlier
investigations. It is perhaps worthy of note that there appears in
Mr Hale’s photographs of detail on the sun’s dise much less per-
spective foreshortening of detail near the sun’s limb than one would
expect to find.
In another arrangement, namely the “coronagraph” used by
Mr Hale at Kenwood, 1893 (Astronomy and Astrophysics, 1894,
p- 673), a modification of the Littrow spectroscope was used. But
the spectroscope was fixed relatively to the sun’s image and to the
photographic plate, and the slits were moved, the nature of the
case being such that the slits move in opposite directions.
1896.] for a form of spectroheliograph. 181
Some modification of Littrow’s spectroscope with fixed slits
would seem obviously the simplest one to use in these investiga-
tions. Iam under the impression that Mr Hale has recorded his
rejection of this form, but I cannot find such a reference. Recent
work with a modification of Littrow’s spectroscope leads me to
believe that the difficulty arising from reflexions from the lens-
surfaces can be overcome by the use of suitable stops. The spectro-
genic apparatus here suggested is accordingly a modification of
Littrow’s spectroscope.
Modification of Littrow’s Spectroscope.
The essence of this form is that one tube and lens serve both
for collimator and for camera or observing telescope.
=; COT
Focussing Screw il
The tube 7' serves as collimator and camera; an object-glass Z
is fitted in a tube 7” which slides in the main tube 7 for focussing
purposes.
A shit A is fitted at one side of the tube 7, its length being
perpendicular to the axis of the collimator; a reflector B placed
near the axis reflects light normally incident on the slit so that
it passes along the axis of the collimator and so through the
object-glass.
A diffraction grating (or a train of prisms with a reflector
at the end) is attached properly to the tube 7’ by means of a
framework K. Light, after falling on the grating (or after a
double passage through the prisms), falls on the object-glass
again and passes along the tube 7’ till it falls on a second re-
flector H, set so as to reflect the light out through the slit F,
which is fixed opposite the first slit. The arrangement is in a
certain sense direct vision; and the line joining the middle points
of the two slits may be called the line of direct wsion; it is of
course perpendicular to the axis of the collimator. (Such a form
of instrument would be convenient for ordinary spectroscopic
182 Mr Newall, On a suggestion [May 25,
purposes, an eyepiece being attached in place of the slit F. It
might be preferable in such a case to have the slits parallel to
the axis of the collimator, a corresponding change being made
in the position of the grating.) For spectroscopic purposes an
achromatic object-glass would be convenient, but for the use of
the instrument in a spectroheliograph a single lens is all that
is needed. A suitable small stop must be set on the inner
surface of the lens near its centre to cut off stray reflected light.
So far as I am aware, it has been the custom in all forms
of spectroheliograph to move the slit slowly across the sun’s dase.
Accurately equable motion is needed in order to avoid streaks
in the resulting photographs—the streaks here referred to are
those parallel to the slit, not those which are perpendicular to
the slit and are due to dust on the slit—and even when the
motion is equable, the effect of a cloud passing in front of the
sun will be to diminish the density of the photograph only in
that part of the disc over which the slit moves during the passage
of the cloud. It often happens that the best definition in solar
observations is obtained when there is considerable haze and even
fog, which is necessarily of varying opacity.
The necessary exposure for the whole disc may be attained
either by moving the slit slowly once across the disc or by letting
the slit pass comparatively quickly backwards and forwards over
it often enough to get the necessary total exposure, the image
of the sun being kept stationary whichever method is adopted.
Mr Hale has adopted the first method, and I am not aware that
the second method has been either tried or suggested. The
oscillatory motion might be given to the slits and connected
spectrogenic apparatus by properly suspending the apparatus
and allowing it to swing like a pendulum. This method involves
the use of a fixed beam of sunlight.
The suggestion which I have to make may be summarized as
follows :—
1. A celostat is to be used to throw a horizontal beam of
sunlight.
2. An object-glass is to be inserted in the beam so as to
form a fixed image of the sun—‘fized’ in the sense connected with
the ccelostat as opposed to the heliostat.
3. The spectrogenic apparatus with fixed slits described and
illustrated above is to be suspended like the bob of some forms
of ballistic pendulums, and in such manner that (a) the slit A
receives the image of the sun upon it, and bisects the circular
disc of the sun when the apparatus is at rest; (b) the line of
1896.] for a form of spectroheliograph. 183
p nad
direct vision as defined on page 181 is horizontal and coincides
in direction with the axis of the horizontal beam of sunlight ;
(c) the slits are vertical. This pendulum is to be set swinging
with an amplitude slightly greater than the diameter of the sun’s
image.
4. A photographic plate is to be set either all but in contact
with the second (monochromatic) slit, or else considerably further
back, with a lens placed between it and the second slit in such
a way as to form an enlarged image of the second slit on the
plate. The lens and photographic plate are to be fixed relatively
to the earth and consequently also to the image of the sun.
The resulting photographs will shew the average appearance of
the disc during the whole exposure. The central parts of the
sun’s disc would get less exposure in a given interval of swinging
than those parts of the borders of the disc at the ends of a hori-
zontal diameter of the image: but this would be no disadvantage
if one considers the difference in brightness between the centre
and the limb. The relation between the exposure at the centre
and near the limb might also be controlled in their small limits by
altering the amplitude of the swing. Loss of definition would
arise either because of atmospheric disturbance, which would affect
the whole disc, or because of violent motions on the sun’s surface,
which would affect only restricted regions on the disc. The
motions appear however to be seldom so great as to be likely
to affect photographs taken with comparatively short exposures,
and on such occasions local loss of definition would indicate the
disturbed regions.
I have hesitated to commit this suggestion to paper without
giving it a practical trial ; my only excuse is that I am in hopes
that some one may be induced to give the method a trial earlier
than I see any prospect of being able to do myself.
(3) On the Period of the Karth’s Free Eulerian Precession.
By J. Larmor, M.A., F.R.S., St John’s College.
1. The main object of this note is to state a principle which
allows us to estimate the effect of elastic yielding of a rotating
solid on the period and character of the free precession of its
axis of rotation. It has been suggested by the recent papers of
Professor Newcomb and Mr Hough!, in which the discussion is
chiefly confined to the case of an incompressible homogeneous
spheroid.
1 §. Newcomb, Monthly Notices R.A.S., 1892; 8S. S. Hough, ‘‘ The Rotation of an
Elastic Spheroid,” Phil. Trans., 1896.
184 Mr Larmor, On the Period of the [May 25,
2. In order to obtain a clear notion of the action of the internal
forcive which causes the free precession, let us examine in a geo-
metrical manner the well-known case of
IL a perfectly rigid solid rotating round its
C axis OC of greatest moment of inertia.
When this motion is disturbed, let OZ
represent the instantaneous axis of the
O rotation w of the solid, and OL the axis
of resultant angular momentum which
is fixed in direction in space. In the
case of a symmetrical solid OC, OI, OL
lie in one plane. With reference to the
solid itself, Of and OL will describe right
cones round OC with common angular velocity ©, that of the free
precession in the solid body of the instantaneous axis of rotation.
The line OL being fixed im space, the point Z of the body will
thus move away from the point Z fixed in space with velocity
—Q.OLsiny, where y represents the angle COL; but as the
body is rotating at the instant round the axis OJ with angular
velocity w, the velocity of its point Z must also be w. OL sin (y — 4),
where y—c represents the angle JOL. Thus we have the geo-
metrical relation
ha
=O isiniy — @isiii (yi) sees eee (Dy
The angular momentum of the rotating solid with respect to
its centre of gravity O is at time ¢ made up of
Cw cose round OC and — Aw sinz round OA.
After an infinitesimal lapse of time 6¢, OC and OA have turned
round the axis OL fixed in space through an angle ’dt say; thus
OC has moved through an angle w’siny. dt, and OA through an
angle w cosy.6t. These changes in the axes of the constant
component angular momenta will introduce two reacting couples,
acting round the same axis perpendicular to the plane COZ and
equal to
Co cost.@’ siny and — Aw sine. cosy:
and in the steady precessional motion these couples must equi-
librate each other, so that
C cosesiny+A sine cosy = 0;
that is, Ctany=A tans
Combining equations (1) and (2),
QO, = @ (cot y sin ¢ — cos ¢)
1896.] Earth's Free Eulerian Precession. 185
Thus the angular velocity of free precession, as seen by an
observer partaking of the motion of the solid’, bears the ratio
(C—A)/A secs to the angular velocity of the rotation: when the
amplitude of the precession is small, the ratio reduces to (C — A)/A.
3. We have now to examine in what respects this argument
is modified when there is elastic yielding to the centrifugal force
of rotation, instead of absolute rigidity. As the period of relaxa-
tion of a strain in the Earth is a fraction of a day, while that of
the Eulerian precession is measured in hundreds of days, it follows
that the distortion due to centrifugal force will follow with great
exactness the movements of the instantaneous axis of rotation:
and the same will usually hold good in other problems of slow
and small free precessional motion. Thus if C’ and dA’ represent
the moments of inertia, round OC and OA, of the configuration
which the body would assume when the strain due to centrifugal
force is removed,—or, what is the same thing, of the configuration
it would assume under the action of an applied bodily forcive
equal and opposite to the centrifugal force of the rotation—the
angular momentum will now be made up of the components,
C’w cose round OC,
— A’w sine round OA,
Io round OJ,
where J is the increase of moment of inertia round OJ due to the
centrifugal bulging.
Thus the reacting couples, in the plane COZ, are
C’w cost. w’ sin y,
— A’wsini. w' cosy,
Io. sin(y—2);
and these must balance. When the axis OJ does not deviate far
from OC, the moment of inertia round it is equal, to the second
order of small quantities, to that round OC; thus J = C—C’, and
the condition for steady precession is therefore
C’ tan y + (C — C’) (tan y — tan ¢) = A’ tan o,
that is, Ctany={C—(C’— A,)} tance;
so that, by the geometrical relation (1)
C’— A’
oi C02) COS bn) o\n vlalelolaleielele(ele=)siain) stele (4).
1 This is different from the precession of OC or OI in space, which is round the
fixed axis OL, and of angular velocity Q', where 2’siny=w sinz.
186 Mr Larmor, On the Period of the [May 25,
The validity of this result is also, as above stated, confined to
the case in which 27/0 sine is large compared with the time of
relaxation of elastic strain in the solid of revolution to which it
belongs.
Since C—C"’ is small compared with C and A, as the elastic
deformation only slightly alters the shape of the body, the third
of these balancing reacting couples can be neglected compared
with the other two. Thus the free precession, under the influence
of elastic yielding, will be the same as would belong to an absolutely
rigid body, whose configuration is the one that the actual solid
would assume were the centrifugal force removed, its elasticity
being supposed unimpaired and the same as actually exists for
smaller distortions.
4. In order that the principle stated in this form may hold
good, it is not necessary that the solid should be symmetrical
round the axis of rotation. The couple due to the elastic defor-
mation by the centrifugal force can be similarly neglected when
the moments of inertia of the solid are all unequal, provided, as
above, the oscillation of its axis of rotation remains small, as will
be the case if it is spinning round the axis of greatest moment
and is but slightly disturbed. Thus, in accordance with Poinsot’s
theorem, the motion may be represented by the rolling of the
modified momental ellipsoid of the solid on a fixed plane; so that
the axis of instantaneous rotation will trace out a small ellipse
on the surface of the rotating body and the precession will there-
fore be exactly periodic’. It follows easily from the Eulerian
equations of motion of a solid free from external forcive, that the
period of the free precessional motion of the axis of rotation
round this ellipse is to that of the rotation of the body in the
A'B 3
ntio ea OLE,
ments of inertia, viz. those that would exist when the strain due
to the centrifugal force is supposed removed as above; agreeing
with the result already given where A’ and BP’ are equal.
where A’, B’, C’ are the effective mo-
> >
5. If when the centrifugal force is thus taken off, the rotating
solid became dynamically symmetrical like a homogeneous sphere,
there would be no free precession at all: if it became effectively
prolate, the precession would be in the negative direction. In
the actual case of the Earth, the precession is in the positive
1 Tt follows from Poinsot’s kinematic representation of the Eulerian motion,
that for any solid rotating with no couples acting on it, the motion of the axis of
rotation in the body itself is in all cases strictly periodic. It is not difficult to
extend this result to the more general case in which there are fly-wheels or other
sources of gyrostatic momentum attached to the solid.
1896. ] Earth's Free Eulerian Precession. 187
direction; which is in agreement with the accepted doctrine that
the Earth assumed originally a form of fluid equilibrium, in which
it has been gradually solidifying, so that were the centrifugal
force now removed it would still retain an oblate form.
6. The practical outcome, as regards Astronomy, is that, as
the precessional constant (C—A)/C of the actual Karth is deter-
mined precisely by the periods of the ordinary astronomical
precessions and nutations, so also the modified precessional
constant (C’—A’)/A’ of the Earth us it would be were the centri-
fugal force of the axial rotation removed, can be estimated from
the period of the free Eulerian precession,—in so far, that is, as
this period can be disentangled from the actual observations of
changes of latitude, which are also affected by large irregular
variations due to meteorological causes, and more or less of an
annual character. As the value of C—A is determined by a
knowledge of the variation of gravity at the Earth’s surface, the
values of C and A are separately known; and therefore the value
of 0’ — A’ is approximately known in terms of the Eulerian period,
thus affording an additional datwm of somewhat precise character
for investigations relating to the physical condition of the Karth’s
interior.
On the other hand, the forced nutations due to extraneous
astronomical forcives, even those of short period, are of course
not sensibly affected by the circumstance that the centrifugal
part of the Earth’s ellipticity follows the movements of the axis
of rotation.
7. The conclusions above stated are restricted to the case of
a solid body, that is, one in which parts which were initially near
together cannot wander far apart during the motion. If a large
portion of the interior is fluid, other considerations will influence
the result!. If the interior of the Earth were all fluid except an
enclosing shell of moderate thickness, say a few hundred miles,
there could be no sensible free steady precession at all, unless the
rigidity of this shell were far beyond any that is actually known.
The slight change of configuration due to transfer of the
centrifugal force to a new axis of rotation, which is here contem-
plated, need not be purely elastic, in order to make the conclusions
valid. It may be in part viscous: but the wide discrepancy
between the actual period of the Earth’s free precession and the
one that would apply to a perfectly rigid Earth is evidence that
this deformation is really in large part elastic. For if elasticity
proportional to, or a function of, strain were entirely absent, then
1 Cf, Kelvin, Math. and Phys, Papers, Vol. ut. p. 132; Hough, Phil, Trans, 1895,
188 Mr Larmor, On the Period of the [May 25,
viscosity proportional to, or a function of, rate of alteration of
strain would (unless its coefficient were excessively large) be
ineffective in preventing the assumption of the configuration of
fluid equilibrium in the slow motions here considered, and free
precession of periodic character would therefore be non-existent.
8. The influence of the mobility of the surface waters on
the period of the free precession has however yet to be considered.
For them also, if they are sufficiently deep, the time of sub-
sidence of a disturbance will be small compared with the period
of the precession: so that the principle already employed will
still have an application. The simplest case to consider first is
that in which the waters cover the whole surface. When the axis
of rotation changes, the centrifugal strain will be shifted to the
new axis; thus the ellipticity of the underlying solid Earth will
be altered owing to its elastic yielding, while that of the ocean
surface will be altered by a different amount easily calculated
from the conditions of fluid equilibrium.
If on the other hand the ocean consisted only of a thin layer,
its law of depth would be changed considerably, and this may
involve sensible currents in it. Taking the angular momentum
arising from the velocity of these currents (which will diminish
the correction due to the surface waters) to be negligible in the
actual case, the precessional couple will be as before that of the
configuration the Earth would assume if the centrifugal force were
removed; it will be that of a spheroid of water with the free
surface that would exist on the removal of that force, together
with that of the underlying solid Earth with its centrifugal force
removed, but with its specific gravity reduced by unity.
If the underlying Earth were absolutely rigid, the effect of
the layer of water on the precessional couple would be to diminish
it by the couple arising from a spheroid of the same density as
water, with ellipticity equal to that part of the ellipticity of the
ocean surface which is due to centrifugal force alone: if the
underlying Earth is yielding, the ellipticity of this effective water-
spheroid must be that of the ocean surface less that of the solid
Earth, both due to centrifugal force. In any case, it is clear that
under these circumstances the free ocean will cause an increase
in the precessional period. ‘This, as above stated, is on the sup-
position that the ocean is on the average deep enough for the
angular momentum of the currents created in the alteration of
its free surface to be neglected: if for stance it were very shallow
it could obviously have no appreciable effect, and that would be
in part because the momentum of the currents would compensate
the effect of altered ellipticity, im part because its surface would
not then have time to attain the equilibrium form.
1896. ] Earth's Free Eulerian Precession. 189
9. The effect of the transference of masses of water by ordinary
ocean currents and other causes has been considered long ago by
Lord Kelvin and Prof. G. H. Darwin, and more recently by Prof.
Newcomb, with the result that such disturbances are amply
sufficient to originate displacements of the Earth’s axis comparable
with the amplitudes of the observed changes of latitude.
10. If the Earth were absolutely rigid but covered throughout
by surface waters, the momental difference C’— A’ which gives
the free precessional velocity would thus be less than the one
C—A which gives the forced astronomical precession, by that of
a spheroid of water of the ellipticity e, (=;1,)! which is due to
centrifugal force alone. This latter spheroid, of semi-axes a(1 — 2e,)
and a(1+4¢,), has the moments of inertia
C= 20H, (r+ 2€,), A,= 20K, bee 44)3
so that for it C,—A,=2a°E\e,, where EH, is the mass of a sphere
of water of the dimensions of the Earth.
11. The potential of the attraction of the actual Earth at
distant points is, by Laplace’s formula,
E A+B+C-3.
V=y/( == 2/3 tis
where # is the Earth’s mass, @ its radius, and yH/a?=g. In the
case of symmetry when A = B, we have thus
Wad) Cad
Y 7 Qr?
(3co?@—1)+...
@ being the co-latitude.
The potential of the centrifugal force of rotation is
V, =r sin’6.
Over the surface of the ocean of ellipticity e, given by
r=a(1+esin’6),
the total potential V+ V, must be constant: thus
= (1 —e sin?) — sii (3 cos?6 — 1) + 4@°a*y sin?@ = const.,
E 3C-A aoa
so that Bie migaty gs OT do°a’y = 0,
which gives C—A=2a7H(e—}3m);
where m= oa/q, is the ratio of centrifugal force to gravity at the
1 Thomson and Tait, § 821.
VON; 1D aN, hie 14
190 Mr Larmor, On the Period of the [May 25,
equator, viz. 1S gg5. The value of e¢, the ellipticity of the sea-
level, is about 5437: so that the value of C—A is just one half of
that which would belong to the actual free surface in the absence
of centrifugal force.
[We observe, incidentally, that
v=" s@K(e-hr Dee eau
sl as Hae 2e sin?0) — 12 (e— 4m) (8 cos? — 1) — wa sin?@
= {1—(3m—e)sin?6},
where g, is the value of g at the Pole; which is Clairaut’s formula
for gravity.
Again, the value of (C—<A)/C, derived from the precession of
the equinoxes, is (003272: thus
C=207E (e—4m)/00327 = 35e7L.
If the Earth were homogeneous of density 54, we should have
C=0-40a?H#: thus the increase of density towards the centre
diminishes the axial moment of inertia by 12 per cent.?]
Thus for the actual Earth, C— A =14Ha?.51,; from which the
value for the centrifugal water spheroid, that is
gee
On 4h= Bae W. siz
is to be deducted, leaving the effective moment reduced in the
ratio of 72 to 82.
In this case therefore of a rigid Earth covered by a fluid ocean,
the period of the free precession would be increased in the ratio
of 82 to 72 or 1:14 to unity by the presence of the surface waters.
In the actual case the surface waters do not cover the whole
Earth, so that this is only a superior limit. Moreover the distri-
bution of surface waters is not symmetrical, so that the result of
deducting the centrifugal spheroid of water will be to leave an
effective solid with moments of inertia all unequal, and the path
of the instantaneous axis of rotation on the Earth will be an
ellipse, not a circle. But one axis of the ellipse cannot possibly
1 Col. Clarke’s Geodesy, p. 305.
2 As quoted from Leyverrier in Thomson and Tait, § 828.
3 As to how this fits with Laplace’s hypothetical law of internal density, cf.
G. H. Darwin, in Thomson and Tait, § 828.
1896.] Earth’s Free Eulerian Precession. 191
exceed the other from this cause by more than 7 per cent., even if
the Earth were rigid.
Actually, the diminution of precessional moment due to the
surface waters will be much reduced by the elastic yielding of the
core, for when the centrifugal force is removed not only the
surface but also the bed of the ocean will diminish in ellipticity,
so that the differential effect will be smaller. It follows therefore
that 6 to 8 per cent. is an outside limit to the actual increase of
period of the precession that can be due to mobility of the surface
waters.
12. On the equilibrium-theory here advanced, the portion of
the ellipticity of the surface waters which arises from centrifugal
force alone, shifts in company with the axis of rotation, thus
causing a tide of the same period as the free precession, as was
first pointed out by Lord Kelvin. The equation of this ellipticity
is r=a(1+e,sin?@), where e,=;!,. Thus a shift 60 in the axis
of rotation involves a change of level dr/d@.60; which is at
the rate of 0°2sin20 of a foot for each second of are. The
reductions of tidal observations in Holland by Bakhuysen, and on
the Pacific and Atlantic coasts of North America by Christie,
made with this object in view, actually gives a tidal component,
of the period of the Eulerian precession, with amplitudes respec-
tively about ‘03, ‘04, and ‘05 of a foot, thus corresponding to a
precessional radius of the order of a quarter of a second of arc,
which is the observed order of magnitude.
The somewhat close agreement which has been found between
the phase of this tide and the phase of the precession tends
towards verifying both that the equilibrium theory here worked
out is sufficient and that the free precession of period 427 days is
fairly constant in amplitude. The amount of the tide as here
computed will however be diminished by the centrifugal yielding
of the solid Earth; though, this diminution being regular, we
should still find that if the precession were quite regular in ampli-
tude, the tide would at each station be proportional to the
amplitude of the precession multiplied by the sine of twice the
latitude. But it would appear from the observed latitude varia-
tions that the amplitude of the precession is altered so irregularly
that the harmonic analysis of a long series of observations can
hardly bring out anything more definite than a sort of mean
amplitude of tide. The actual tide thus produced follows, on the
equilibrium theory, the movement of the Pole exactly; but it
can only be disentangled from the observations of aggregate tide
by an assumption that it is of a periodic harmonic character.
1 Collected Papers, Vol. 111. p. 332.
192 Mr Larmor, On the Period of the [May 25,
Were it possible to pick out this tide with fair approximation,
we should be able to derive information as to how much the
surface of the solid Earth yields to the centrifugal force.
13. In all the foregoing, the relaxation of strain in the Earth
that would follow the removal of the centrifugal force means such
change of strain as would occur if the materials retained their
existing moduli of elasticity and were of unlimited strength. As
a matter of fact, a removal of the centrifugal force of the Earth’s
rotation would result in strains so great that the solid constitution
of the interior would break down, and the materials would flow
into new configurations in which the straims would be eased. In
so far in fact as the configuration actually existing 1s due to
consolidation from a fluid form, there can be in it no internal
stresses other than simple hydrostatic pressure. In all the
previous argument, what has been really considered has been the
very slight change of configuration arising from a very slight
shift of the axis of rotation: and we can treat of that as the
difference of the centrifugal strains that would belong to the two
positions of that axis, when we assume the elastic constants to be
the actual ones that belong to small strains, and any limitation of
elastic strength is ignored. The question of imperfect elasticity
thus hardly comes up at all in such a case.
14. The question as to whether the interior of the Earth is
in the main solid or fluid, is, when precisely expressed, really a
question as to what intensity of deforming stress will make the
materials in its interior begin to flow. Every actual solid sub-
stance has its own elastic limit: and when subject to deforming
forces sufficiently beyond this limit, the substance will flow lke oil.
The result here arrived at is that for the small stresses involved
in the shght changes of the axis of rotation that accompany the
free precession,—stresses that are of the order of a moderate
number of grammes per square centimetre—the materials of the
Earth’s interior are solid and elastic, and as will appear below
(§ 16) of very high rigidity. Beyond a certain limit they must
give way and flow: the stresses due to the astronomical pre-
cessional forces are not however in the main beyond this limit.
As the Earth slowly alters its form owing to change in the
distribution of surface materials and loss of heat, strains will
arise in its interior and slowly imcrease until the material gives
way somewhere, with earthquake-like effects. At such a weak
place there may be a great deal of strain-energy degraded into
heat, sufficient it may be to melt the material. The region
under a range of volcanic mountains may have a plane of weak-
ness of this kind, up which the molten material is forced to the
1896. | Earth’s Free Eulerian Precession. 193
surface; which finally heals up after the surrounding stress is
reduced in the main to hydrostatic pressure.
15. It has been estimated by Mr Hough! that, were the
Earth a homogeneous solid with the actual surface ellipticity, the
Chandler period for the free precession would require that it
should have the rigidity of steel. The order of magnitude of
this result will not be entirely altered by actual heterogeneity: so
that, if we can assume the correctness of this period, we may
conclude that, as regards the slight stresses here involved, the
Earth is an elastic solid of about the same order of rigidity as
steel. This is in fair accord with the observations of seismologists’,
who find that earthquake shocks are propagated to distant parts
of the Earth not only by the ordinary surface waves, but also by
minute tremors which enormously outrun the earthquake proper,
arriving in a time that would correspond to propagation in a
straight line across the interior of the Karth, provided it possessed
an average rigidity about 4 of that of steel.
(4) Note on a point in theoretical dynanucs. By Sir
RosBeERT Batt.
Let « be a screw about which a free rigid body is made to
twist in consequence of an impulsive wrench administered on some
other screw 7. Except in the case where « and 7 are reciprocal it
will always be possible (in many different ways) to design and
place a rigid body so that two arbitrarily chosen screws a and 9
will possess the required relation.
Let now 8 and € be two other screws (not reciprocal) ; we may
consider the question as to whether a rigid body can be designed
and placed so that a shall be the instantaneous screw correspond-
ing to 7 as an impulsive screw while 8 bears the same relation
to &.
It is easy to see that it will not generally be possible for a, 8,
n, € to stand in the required relations. For taking a and # as
given there are five disposable quantities in the choice of 7 and five
more in the choice of & We ought therefore to have ten dis-
posable coordinates for the designing and the placing of the mgid
body. But there are not so many. We have three for the co-
ordinates of its centre of gravity, three for the directions of its
principal axes, and three more for the radi of gyration. The mass
of the body is not disposable. The other nine quantities being
assigned the relations of the impulsive and instantaneous screws, as
1 Loc. cit. Phil. Trans., 1896.
2 Cf. Prof. Milne, Brit. Assoc. Report, 1896, ‘‘On HKarthquake Phenomena.”
194 Sir Robert Ball, Note on a [May 25,
geometrical entities, are not affected by alterations in the mass.
This produces its effect in the twist velocity acquired and not in
the position of the screw.
It thus appears that if the four screws had been chosen
arbitrarily we should have ten conditions to satisfy and only nine
disposable coordinates. It is hence plain that the four screws
cannot be chosen quite arbitrarily. They must be in some way
restricted. The object of the present note is to shew that these
restrictions are two in number and to set down what they are.
Draw a cylindroid A through a, 8, and another cylindroid P
through 7, & Then an impulsive wrench about any screw w on P
will make the body twist about some screw 6 on A. As moves
over P so will its correspondent @ travel over A. It is easy to
shew that any four screws on P will be equi-anharmonic with
their five correspondents on A, and that consequently the two
systems will be homographic.
In general to establish the homography of two cylindroids
three corresponding pairs of screws must be given. And of course
there could be a triply infinite variety in the possible homo-
graphies. It is however a somewhat remarkable fact that in the
particular homography with which we are concerned there is no
arbitrary element. Given two cylindroids A and P, then without
any other considerations whatever all the corresponding pairs are
determined. This is first to be proved.
If the mass be one unit and the intensity of the 1mpulsive
wrench on @ be one unit then the twist velocity acquired by @ is
cos (@w)
Poe
where cos(@m) denotes the cosine of the angle between the two
screws @ and w and where py is the pitch of 6. If therefore py be
zero then cos(@@) must be zero. In other words, the two impulsive
screws @,, @, on P which correspond to the two screws of zero
pitch @,, @, on A must be at right angles to them respectively.
This will at once identify the correspondents on P to two known
screws on A.
We have thus determined two pairs of correspondents, and we
can now find a third pair. For if @; be a screw on P reciprocal to @,
then its correspondent @; will be reciprocal to @,. Thus we have
three pairs 6,, 6,, 0; on A, and their three correspondents @,, @2, @;
on P. This establishes the homography, and the correspondent @
to any other screw @ is assigned by the condition that the anhar-
monic ratio of @,, @,, @;, @ 1s the same as that of 6,, 0, 0, @.
1896.] point in theoretical dynamics. 195
Reverting to our original screws a and », 8 and &, we now see
that they must fulfil the conditions
(w,a.@3n) = (0,0,0.0),
(@,@.@3€) > (0,0,0,8),
where the quantities in the brackets denote the anharmonic ratios.
On working out the relations they assume the simple forms
Pa
Cos (an)
cos (Bn) + ede) cos (a&) = aug,
Pa ely SB
cos (an) ”°" ~~ cos (BE)
where w,g denotes as usual the virtual coefficient of the two screws
a and £.
I had already given the second of these equations in the Tenth
Memoir on the Theory of Screws, Trans. Royal Irish Academy,
Vol. xxx., p. 571. I did not then know that there must be the
further condition represented by the first. Nor was I then aware
of the definite homography between the screws on two cylindroids
which expressed the geometrical conditions under which alone one
of these cylindroids could be the locus of impulsive screws cor-
responding to the screws of the other as instantaneous screws.
(5) On the maximum deviation of a ray of light by a prism.
By Prof. A. ANDERSON, M.A., Sidney Sussex College.
Let the great circle VV, be the principal plane of the prism,
N, and NV, the normals to the faces. With NV, and J, as centres
196 Prof. Anderson, On the maximum [May 25,
describe small circles with radii equal to the critical angle. These
circles must intersect if it be possible for a ray to get through,
and the point & representing the direction of the ray in the prism
lies on the part of the sphere common to the areas of the circles.
Draw a small circle whose distance from N,N, is 7’ the angle
which any ray in the prism makes with the principal plane, and
let it intersect the two small circles already drawn in # and F.
Then for positions of R on HF, G the middle point 1s that which
corresponds to minimum deviation and /, # are the points cor-
responding to maximum deviation’. Hence to find the absolute
maximum deviation we must examine the values of the deviation
for positions of R on the small circle CA.
Let R be one of these positions. Join V,R and take V,P a
A A
right angle. Join VR and produce so that sin V,Q =p sin N.R.
Then P is the direction of the incident ray and @ that of the
emergent ray, PQ being the deviation.
Let PQ=6, V.R=¢, RQ =84; then if A be the angle of the
prism it is easy to shew that
j sin 0
cos 6 = (uw2—1) cos A GAG —p?+1+ pcos 6.
The deviation is therefore stationary when
sin 8
A ——;
cosy cos A 5 + cos 0
18 stationary, which may be shewn to hold when
cos A sin ¢ = tan y sin 0,
a condition equivalent to
1 + cos?A
2 cos A
Since 1 + cos?-A >2cos A, the necessary condition ¢<y is
satisfied.
We may easily find for what values of the angle of the prism
cos d = cos ¥
a stationary value of 6 is possible. Since cos ¢ is positive, A <3.
Again, the least value of the variable ¢ is A —y or y—A and
consequently
1 + cos’A
2 cos A
which reduces to tan A < 2 tan y.
cosy. < cos (A —y¥),
1 Proc. Camb. Phil. Soc. ix. p. 109.
1896.] deviation of a ray of light by a prism. 197
Supposing these conditions to hold, we must find whether the
value of ¢ given by
1+cos?A
' 2cos A
corresponds to a minimum or a maximum value of the maximum
deviations. Denoting the expression
cos @ = cos
sin 0
cos y cos A aie + cos 6
by WV, we have
oe sin 0
dé cos(0+¢)siny cos y cos A Besiy soa
The quantity in brackets is zero when cos ¢ = cos y.
sin @ — sin 6 sin y].
1+cos?A
12 cos) Aly?
positive when ¢ is less than the value given by this equation, and
negative for greater values. The value of ¢ given by the above
equation corresponds then to a maximum value of WV and con-
sequently to a minimum value of the maximum deviations. The
absolute maximum deviation corresponds therefore to that one of
the points - and A for which the deviation is greatest.
feet 2 5° is negative for all values of ¢ and therefore V
diminishes from C to A. The absolute maximum deviation cor-
responds therefore to the poimt A and is given by
sing =VeaI sin4,
If A > tan(2 tan y) the quantity in brackets is always negative
and the absolute maximum deviation again corresponds to A with
the same value as for the last case.
As examples of the first case, which is of greater interest than
the others, take two glass prisms one of 20° and the other of 50”,
and assume the critical angle to be approximately 42°. With
this value of the critical angle the angle of the prism must be
< 60° 57’ for a stationary value of the maximum deviations to
exist. For the first prism the deviation corresponding to the
point A is found to be 22° 24’ and for the point C 35° 50’. The
maximum deviation is accordingly 35° 50’. For the second prism,
on the other hand, the deviation corresponding to A is greater
than that corresponding to C, the values being respectively 56° 23’
and 46° 3’. It is easy to write down an inequality involving the
angle of the prism and yu, separating cases where the absolute
maximum deviation corresponds to the point A from those in
which it corresponds to C, but it does not seem capable of concise
expression.
VOL, 1X. PART It, 15
198 Mr Dixon, On a method of discussing [May 25,
(6) Ona method of discussing the plane sections of surfaces.
By A. C. Drxon, M.A., Trinity College.
The plane sections of surfaces are generally treated by examin-
ing their projections upon one of the co-ordinate planes. It is
possible however to find at once the equation to any section of
any surface referred to any axes, or indeed to any triangle, in its
plane.
Let (a, 41, 21) (2, Yo, 22) (3, Ys, 23) be the co-ordinates of the
three vertices of the proposed triangle of reference referred to
the original axes. Let (u, v, w) be the areal co-ordinates of any
point in the plane of the triangle referred to that triangle. Then
the co-ordinates of the same point referred to the original axes are
(Ua, + Vy + Ws, Wy + VYo + WYs, UZ + VZ_ + Ws).
By substituting these for a, y, z in the equation to any surface
we have the equation, in areal co-ordinates, to the section of the
surface made by the plane of the triangle.
As an application—if we write down the condition that this
curve should have a double point and in this condition suppose
£3, Y3, 2, to be current co-ordinates we have an equation which
will represent the tangent planes that can be drawn to the surface
through the straight line joining (a, y;, 2) to (#2, Yo, 22).
Thus for a conicoid we have the equation to a pair of tangent
planes in the form
S50 Si5 Sb i=,
Si, Sansa
Sp Sia | (Sb
S=0 being the equation to the surface itself, and
(Si, Sing Shap Sin, Say Sa Od, oh PaO
the areal equation to the section.
If we wish to have Cartesian instead of areal co-ordinates in
the plane, suppose (&, 7, €) to be the origin and (J, m, %) (ls, mo, Ne)
the direction-cosines of the axes, rectangular or oblique. Denote
the co-ordinates in the plane by (uw, v) and the co-ordinates of the
same point referred to the old axes are
(E+ ]Lut+ly, n+ mut mv, €+nuwt+ nv).
For instance, let us consider a plane section of the surface
aa? + by? + cz? =1.
1896.] the plane sections of surfaces. 199
Let (A, #,v) be the direction-cosines of the normal to the plane
of the section.
The equation is
a(E+lu+ lw) + b(n +mu+ mv)? + ¢(€+nu+ny)?=1.
As &,7, € do not enter into the highest terms, all parallel
sections must be similar and similarly situated conics.
Suppose the origin to be the centre; then
a&l, + bnm, + cfr, = 0,
a&l, + bym, + cn, = 0,
so that = = a xe ;
py ae
Thus the locus of the centre of a section parallel to a given
one is a straight line through the centre of the surface.
If the axes of the section are the axes of w and v, we have
abl, + bmyms, + enyns = 0,
Ll.+ mym,+ N= 0,
Ll, mM, __ NN
or = = :
b—c c—a a-—b
Substitute for (,,m.,.) in the equation Al, + pm, + vn, = 0,
and we find
b—c c—a a—b
Xr = v
l, fe Mm, Ny
as the equation that determines the directions of the axes of the
section in terms of A, p, v.
Or we may eliminate (/,, m., n.) by means of multipliers and
write
al, =pl,t+or, bm, =pm,+ op, cm =pn,+or.
Thus p=al? + bm,? + cn,’,
so that (1 — a&? — bn? — c&?)/p is the square of the semi-axis in the
direction (0,, 7m, 1%); l, 7, m, are proportional to
Xr pw v
a—p’ b—p’ c—p’
dA? Va yp
and ilies
a—p b—p cp
If the section is a circle we have
a (0,7 — 1,7) + b (m,? — m2) + ¢ (n,? — n,”) = 0,
all, + bmym, + cnn, = 0.
200 Mr Dizon, On a method, etc. [May 25, 1896.
From these eliminate c. Thus
& (Ml. — Nol1) (Ml, + Nate) = b (M,N, — Msn) (MN, + M<yN2),
or arp = bruv.
By symmetry each = cdr.
Thus, unless the surface is a sphere, ’ or w or v= 0.
These examples will perhaps be enough to illustrate the
method, which is an extension of that of Joachimsthal, so freely
used by Dr Salmon.
PROCEEDINGS
OF THE
Cambridge Philosophical Society.
ANNUAL GENERAL MEETING.
Monday, 26 October, 1896.
PROFESSOR HUGHES, VICE-PRESIDENT, IN THE CHAIR.
The following officers and new members of Council were
elected :—
President :
Mr F. Darwin.
Vice-Presidents :
Prof. G. D. Liveing, Prof. Newton, Prof. J. J. Thomson.
Treasurer:
Mr Glazebrook.
Secretaries :
Mr Newall, Mr Bateson, Mr Baker.
New Members of Council:
Dr Gaskell, Mr Marr, Mr Larmor, Dr Marshall Ward, Mr Shipley.
Mr F. Darw1y, President, then took the Chair.
The names of the Benefactors were read.
VOL. DX. PT. IV. 16
202 Mr Harmer, On the casts of [Oct. 26,
The following Communications were made to the Society:
(1) On the casts of Iguanodon bernissartensis, Boulenger,
recently presented to the Museum of Zoology by H.M. the King of
the Belgians. By S. F. Harmer, M.A., Superintendent of the
Museum of Zoology.
Mr S.‘F. Harmer exhibited the casts graciously presented to
the Museum of Zoology by His Majesty the King of the Belgians.
The casts, which are reproductions of some of the famous specimens
preserved in the “ Musée Royal d’ Histoire Naturelle de Belgique,”
at Brussels, were specially prepared for the University under the
supervision of M. Dupont, the Director of that Museum; and they
constitute an entire skeleton, together with supplementary casts
of the skull, lower jaw, ium and some other bones. The gift
included the elaborate iron-work necessary for the support of the
skeleton, which is a copy of the specimen figured in the Bull.
Mus. Roy. d Hist. Nat. de Belgique, Tome 11. 1883, Pl. v. (See
also p. 120 of the same Volume.)
A letter announcing the receipt of this magnificent donation
was written. to the Vice-Chancellor on August 12, 1896; and is
published in the Cambridge University Reporter, 1896—97, p. 20.
The originals were discovered in April, 1878, in the colliery of
Bernissart, a village situated between Mons and Tournai, close to
the French frontier. The bones, which are of Wealden age, were
found at a depth of 356 metres (822 metres below sea-level). A
notice of their discovery was communicated to the Belgian
Academy’ on May 7, 1878, by Professor Van Beneden, who had
recognized them as probably belonging to Jguanodon. A fuller
account was communicated to the Academy, later in the same
year, by M. Dupont?, Director of the Brussels Museum. M. Dupont
announces the discovery of five skeletons, a number which has
since then been increased to nearly thirty, all of which appear to
have been full-grown. The majority of the specimens belonged to
a new species, I. bernissartensis, Boulenger®, the specific distinct-
ness of which has been later maintained by Dollo*; while the
others belonged to I. mantelli, well known in England through
the labours of Mantell, Owen and others.
The bones were in a very friable state ; and it was necessary to
subdivide the clay in which they were lying, into blocks, which
were then surrounded by plaster of Paris. In this condition the
1 Van Beneden, P. J.: ‘‘Sur la découverte de reptiles fossiles gigantesques dans
le charbonnage de-Bernissart”’; Bull. Ac. Roy. Belgique, 2 Sér., xiv. 1878, p. 578.
2 Dupont, H.: “Sur la découverte d’ossements d’Iguanodon,” Ibid. 2 Sér., xivt.
1878, p. 387. 5
® Ibid. 3 Sér., 1. 1881, p. 606.
* Bull. Mus. d@ Hist. Nat. Belgique, 1. 1882, p. 161.
1896.] Iguanodon bernissartensis, Boulenger. 203
blocks were brought to the surface, having previously been num-
bered so that they could afterwards be rearranged in their proper
relative positions. On removing the plaster the bones were
exposed, and treated in the manner necessary for their preser-
vation. The whole process was carried out with the greatest care
and skill; so that, instead of obtaining merely a few of the best
preserved bones, the Museum at Brussels is now in possession of
the entire series of more or less complete skeletons, five of which
are actually mounted in one of their public galleries.
The genus Jguanodon was founded in 1825, by G. Mantell},
who described the teeth of this animal from Wealden formations
in Sussex ; and suggested the generic name in consequence of the
resemblance of the teeth to those of the Iguana. Our knowledge
of the genus was largely increased in later years by the discovery
of numerous remains of J. mantelli and probably other species? in
the Wealden strata of Kent, Sussex and the Isle of Wight. These
fossils were for the most part described by Owen, and their
description occupies no inconsiderable part of the Monographs
published for that author by the Palaeontographical Society®.
The same formations were known to contain the three-toed foot-
prints of gigantic bipedal animals. These footprints, long sus-
pected to have been formed by Jguanodon, may now be definitely
considered to have belonged to that animal.
Although much had been done, in England and elsewhere,
towards understanding the structure of Zguanodon, no skeleton
which was more than fragmentary had been described before the
Belgian discoveries were made. The magnificent series which has
been made available for scientific study, owing to the well-directed
energy of the Brussels Museum, has resulted in making the bony
structure of Zguanodon almost as well known as if it had been a
recent species’. The Museum of Zoology is highly favoured in
having received this splendid present. The group of the Dinosauria
were hitherto entirely unrepresented in the Museum; and J/qua-
nodon is of the greatest importance as an educational object, not
merely from its immense size, but because of the striking resem-
blances which it shows to Birds in certain parts of its structure.
1 Phil. Trans. 1825, Part 1. p. 184.
2 Cf. Lydekker, R.: ‘‘Cat. of the Fossil Reptilia and Amphibia in the British
Museum,” Part 1. 1888, p. 195.
3 **Monograph on the Fossil Reptilia of the Cretaceous Formations,” Part 1.
1851, p. 105; ibid. Suppl. 11. 1861, p. 27; ‘‘Monograph on the Fossil Reptilia of
the Wealden and Purbeck Formations,” Part 11. 1855; ibid. Suppl. 1. 1858;
ibid. Suppl. 11. 1859 (as Streptospondylus); ibid. Suppl. 11. 1864; ibid. Suppl. rv.
1872; ibid. Suppl. v. 1874.
4 The specimens found at Bernissart have been described by Dr L. Dollo in
a series of papers published in the Bull. Mus. d’Hist. Nat. Belgique (Vol. 1. 1882,
pp. 161, 205; Vol. 11. 1883, pp. 13, 85, 223; Vol. 11. 1885, p. 129); also in Arch. de
Biol. vi. 1887, p. 249; Bull. Sci. France et Belgique x1x. (3 Sér. 1.), 1888, p. 215;
and elsewhere.
16—2
204 Mr Gadow, On the supposed relationship [Oct. 26,
(2) Remarks on the supposed relationship of Birds and
Dinosaurs. By H. Gapvow, M.A., Ph. D., FBS.
It is least objectionable to divide the enormous order of
Dinosauri into the following four groups.
I. Sauropoda. Premaxilla with teeth. Pubis single, with
symphysis.
Fore- and hindlimbs pentadactyle and of the walking type,
plantigrade.
Tarsalia free.
Hereto belong: Atlantosaurus, Brontosaurus, Morosaurus, Dip-
lodocus, mostly gigantic beasts from the Upper Jurassic of
Wyoming. Ornithopsis from the English Wealden.—These genera
of Sauropoda are not the ancestors of the other Dinosaurs.
II. Theropoda. Carnivorous. Premaxilla with teeth. Pubis
simple, with symphysis.
Forelimbs shorter than the hindlimbs; digitigrade, with fre-
quently pronounced upright gait. The first and fifth metatarsals
and toes are often reduced. Proximal tarsalia with the tendency
to fuse with the tibia; the astragalus sometimes with an ascending
process. Metatarsals elongated and sometimes fused with each
other.
Hereto belong: Anchisaurus, from the Upper Triassic of
Connecticut; in the same level of which are the Ornithichnites
(Brontozoum giganteum). Zanclodon from the Keuper of Wuert-
temberg. Megalosaurus from the Oolite of Europe and Colorado.
Allosaurus, Ceratosaurus, Coelurus, Hallopus from the Upper
Jurassic of North America—Compsognathus from the Bavarian
Oolite : long neck, with slender ribs. Forelimbs much shortened,
but only three clawed fingers are known. The whole hindlimb is
almost typically avine; the astragalus has an ascending process
and is fused with the tibia; the distal tarsalia are fused with the
metatarsalia. The 2nd, 38rd and 4th metatarsalia are much
elongated and fused with each other, the 5th is very vestigial, and
the 1st 1s much reduced proximally and carries the hallux which
is placed backwards. The four toes have 2, 3;4 and 4 (not 5)
phalanges. The fibula is slender. The femur mostly with an
inner (fourth) trochanter.
III. Orthopoda. Herbivorous. Premaxilla without teeth.
With a premandibular edentulous piece, the so-called predentary
bone, which is probably a calcified horny pad. Each pubis consists
of an anterior and a posterior arm, the so-called prepubis (homolo-
_ gous with the “pubis” of most recent Reptiles and the pectineal
process of Birds) and the postpubis (homologous with the pro-
cessus lateralis pubis of Chelonians and Saurians, and with the
1896.] of Birds and Dinosaurs. 205
“pubis” of Birds). The right and left pubes form no symphysis
but remain widely asunder.
A. Stegosauri: Plantigrade. ‘Tarsals and metatarsals free.
Sometimes three-toed. Forelimbs massive, not much shortened.
— With a dermal armour.
Scelidosaurus from the Lias to the Chalk, in England.
Stegosaurus from the Jurassic of North America.
B. Ornithopoda. Forelimbs much shorter than the hindlimbs,
but stout and pentadactyle. Hindlimbs elongated; digitigrade.
Femur with a fourth trochanter.
Camptosaurus and Luosaurus from the Upper Jurassic of North
America. Tarsals and metatarsals free. Fifth toe lost, first not
functional; number of phalanges of the first to fourth toes 2,
3, 4, 5.
Hypsilophodon, from the English Wealden. Metacarpals
short, the fifth vestigial; the four fingers with 2, 3, 4, 2 phalanges ;
first and fourth fingers much reduced. Astragalus and calcaneus
separate. Metatarsals elongated, free; fifth vestigial. Toes with
2, 3, 4, 5 phalanges.
Iguanodon. Wealden of Europe. Astragalus, calcaneus and
distal tarsals free. Metatarsals free, first styliform, fifth lost.
Toes with 3, 4, 5 phalanges.
Hadrosaurus and Diclonius, from the Upper Cretaceous of
North America; allied forms in Europe. The most differentiated
of all Ornithopoda, as shown by its bill.
Ornithomimus. Upper Cretaceous of Colorado. The systematic
position of this creature must remain doubtful, only the fore- and
hindlimbs, without their girdles, being known. The metatarsals,
of which only the second, third and fourth are developed, are much
elongated ; the third is, with its proximal half, pushed back between
the second and fourth, exactly as in Birds. The astragalus has an
ascending process and is fused with the tibia. The fibula is very
slender.
IV. Ceratopsia. Marsh. Pubis simple, with symphysis.
Femur without inner or fourth trochanter. Forelimbs very little
shorter than the hindlimbs. Pentadactyle, quadrupedous.—Man-
dible with a toothless “ predental” and premaxilla, likewise with a
toothless separate element, the so-called os rostrale——With dermal
armour. Skull “horned.”
The Ceratopsia consequently combine characters of the Sauro-
poda and Orthopoda; their occurrence in the Cretaceous for-
mations of Europe and of North America, justifies us in treating
them as a separate group of the Dinosauri.
Ceratops and Triceratops from Europe and North America.
It is easy to select a considerable number of characters amongst
the various Dinosaurs, which also reoccur in Birds, and some of
206 Mr Gadow, On the supposed relationship [Oct. 26,
which had until a recent date been considered as peculiar to
Birds.
The double two-armed pubic bones: all the Orthopoda.
The increased number of vertebrae to which the long ilia are
attached: most of the Dinosaurs with an upright gait.
The upright gait itself: Orthopoda and most Theropoda.
The possession of ascending process of the so-called astragalus
and its fusion with the tibia: Compsognathus and Ceratosaurus
among Theropoda; and in Ornithomimus.
Fusion of the proximal tarsalia with the tibia and fibula:
Anchisaurus.
Attachment of the distal tarsalia to the metatarsalia: Comp-
sognathus.
Vestigial condition, or absence of the fifth metatarsal : Anchi-
saurus, Compsognathus, Scelidosaurus, Iguanodon.
Backward position of the hallux, and proximal reduction of its
metatarsal : Compsognathus.
The proximal half of the third metatarsal is pressed back
between the second and fourth: Ornithomimus.
The functional metatarsals are much elongated and more or
less fused with each other: Compsognathus, Ceratosaurus.
The phalangeal numbers of the second to fourth toes, namely
2, 3, 4, 5: Camptosaurus and Laosaurus; 3, 4, 5 in Iguanodon.
It would be a very unscientific, but unfortunately not un-
precedented, procedure to take all these numerous resemblances
together, and to conclude that Birds have descended from Dino-
saurs. Huxley was the first to show clearly that Birds have
sprung from a Reptilian stock, and he said of the Dinosaurs,
especially his “ Ornithoscelidae” (Iguanodon, Scelidosaurus, Ha-
drosaurus, Megalosaurus, Compsognathus, among others) that they
“present a large series of modifications intermediate in structure
between existing Reptilia and Aves” (Manual of Anatomy of
Vertebrated Animals, London, 1871, p. 223). Since that time our
knowledge of the Dinosaurs has been enormously increased. Baur
(Morphol. Jahrbuch, Vol. vit. 1882; “ Der Tarsus der Voegel und
Dinosaurier’) proved to his own satisfaction “dass die Dinosaurier
in Wirklichkeit die Stammeltern der Voegel sind, glaube ich nach
meinen Untersuchungen als sicher hinstellen zu duerfen,” and he
stuck to the same view in two shorter papers in Morphol. Jahrb. x. —
1885, in answer to Professor Dames’ criticisms (Archaeopteryx, in
Palaeontolog. Abhandl., Vol. 11 1885; and Morphol. Jahrb. X.).
In Morph. Jahrb. x. p. 615, Baur said “In den herbivoren Dino-
sauriern, speciell in den ornithopodenaehnlichen Formen, haben
wir die Stammeltern der Voegel zu suchen, und zwar die Stamm-
eltern der Ratiten, waehrend wir die Carinaten als von den
Ratiten abstammend betrachten.” He has since given up this
1896.] . of Birds and Dinosaurs. 207
view. Nor is the descent of Birds from any known group of
Dinosaurs favoured by K. v. Zittel in his Handbuch der Palaeon- .
tologie, or by Haeckel in his recent work Systematische Phylogenie
der Wirbelthere.
Nevertheless this notion of the Dinosaurian ancestry of, and
especially Iguanodont relationship of Birds has got hold of many
people’s minds, thanks to various popular and not overeritical
writers. The picture of the Iguanodon, side by side with that of
a Dinorius or Moa, makes a powerful appeal.
The oldest bird known is Archaeopteryx, from the Oolite of
Bavaria. Consequently all those Dinosaurs which are of Oolitic
and later date have to be excluded from the supposed ancestry,
and they happen to be those in which (as in Ceratosaurus,
Compsognathus, Iguanodon, Ornithomimus) the resemblances are
greatest. There remain only Anchisaurus of the Rhaetic, the
contemporary of the unknown Brontozoum which left its three-toed
footprints, and Anchisaurus disagrees from birds in its pelvis.
Zanclodon of the Keuper is also one of the Theropoda. Moreover
the most bird-like foot is either that of one of the Theropoda
(which are excluded by their pelvis) or of some of the latest
Ornithopoda. The upright walk, which has been assumed and
improved upon independently by members of both Theropoda and
Orthopoda, has produced the same, or nearly the same modifications
in them as in the birds. A splendid lesson in isomorphism, homo-
plasy, or convergent analogies. The common substratum from
which all the Dinosaurs and the Birds have sprung, have been of
course some pentadactyle, plantigrade, four-footed Reptiles. The
movable quadrate of birds, firmly fixed in Chelonia, Crocodilia,
Sphenodon, Dinosaurs and Theromorpha, hardly points in their
direction.
Lastly, they who entertain the Dinosaurian ancestry of Birds
seem to forget, or at least they do not fully appreciate -the enor-
mous differences between the forelimb of Archaeopteryx and that
of any Dinosaur with avine resemblances in the hindlimbs. The
forelimbs of these Dinosaurs are already developed in a direction
diametrically opposed to that from which a bird-hke wing could
be developed. ‘To reconcile the wing of a Bat with the foreleg
of a Cow, we have to go back to the indifferent pentadactyle type.
The skull presents another difficulty, and here again Comp-
sognathus comes perhaps nearest to that of a generalised bird’s
skull; and that the Jurassic Archaeopteryx and the Cretaceous
Hesperornis have teeth in the anterior portion of the mandible,
seems to exclude the Orthopoda in which the toothless, padded,
front portion of the underjaw is such a universal feature.
It can of course be assumed, for argument’s sake, that the
ancestors of Birds were a group of Reptiles with an upright gait,
208 Mr Harmer, On Cyclostomatous Polyzoa.. (Oct. 26,
with tarsal and metatarsal bones still free, with a quadrate bone
not yet fixed, without upper and lateral separate temporal-parietal
fossae, with a bifurcated pubis, with a complete alveolar dentition,
—but would we call such creatures Dinosaurs, and if so, where are
they ?
(3) Notes on Cyclostomatous Polyzoa. By S. F. HARMER, M.A,
King’s College.
(Received Nov. 5, 1896.)
On a former occasion I announced to this Society the occur-
rence of embryonic fission as a normal feature in the development
of Crisia*. Since that time I have accumulated fresh evidence”
tending to show that the process then described is, with various
modifications, characteristic of the Cyclostomata im general. My
most recent observations, on [dmonea serpens, L., although by no
means completed, have led to results which appear to me not
unworthy of the acceptance of the Society.
The ovicell of J. serpens belongs to a type which is, in many
respects, intermediate between that of Crisia and that of Licheno-
pora. The colony grows as a lobed encrustation on other objects,
and each lobe usually develops an ovicell, which in its fully-
developed form appears as a punctate calcareous film extending
between the bases of the more distal zocecia. The tubular aperture
does not develop until the ovicell has reached an advanced stage
of development. The morphology of this type of ovicell has not
hitherto been sufficiently studied.
As in the case of Crista and of Lichenopora the ovicell begins to
develop before it can be recognized externally, since it is at first
in no way distinguishable from a zoceclum. ‘There can in fact be
little doubt that the entire ovicell is a much modified zocecium,
its tubular aperture corresponding with the orifice of an ordinary
zocecium.
Sections through the growing edges of vigorous colonies, in the
breeding season, commonly reveal the presence of egg-cells in
connexion with the caecum of the stomach of many of the younger
polypides and buds. These eggs are precisely similar to those
which I have observed in other Cyclostomes, or to those which
had previously been described, by Claparede’, for instance, in the
young buds of Bugula. One, two or three eggs are present in
each fertile polypide, and each is enclosed in a distinct follicle.
The eggs appear in the very young polypide-buds, and in all cases
observed, those which are in connexion with the younger polypides
show no trace of nuclear division. In the eggs of recently mature
1 Proc. Cambridge Phil. Soc. v11. 1892, p. 48 [read Feb. 10, 1890].
2 Quart. J. Micr. Sci. xxxiv. 1893, p. 199; xxxrx. Part 1. 1896, p. 71.
3 Zeitsch. f. wiss. Zool. xx1. 1871, p. 166.
1896.] Mr Harmer, On Cyclostomatous Polyzoa. 209
polypides, whose rectum already contains the remains of Diatoms,
I have found evidence of the division of the nucleus of one of the
eggs, as well as some indication that the other eggs (if any) of the
same individual are degenerating. The development of an egg
takes place, however, in a very small proportion of the ovigerous
polypides, as is shown by the small number of ovicells and by the
fact that each ovicell contains but a single “embryophore’*.”
The next stage is the degeneration of the fertile polypide, as
in Lichenopora. Up to this time, there has been no external
difference between the young ovicell and an ordinary zocecium ;
but after this stage the ovicell becomes easily recognizable as such.
The punctate, calcareous film is the outer wall of a cavity con-
tinuous with the cavity of the fertile zocecium ; and this structure,
usually described as the “ovicell” or “ocecium,” is thus merely a
dilated part of that zocecium. The young ovicell contains a small
brown body, the result of the degeneration of the fertile polypide,
with which are connected various structures, together composing
the embryophore. The latter differs considerably in detail from
that of either Crista or Lichenopora, but parts corresponding with
the “tentacle-sheath” and the “follicle” of the former and with’
the “suspensor” of the latter can be recognized. In a late stage
the embryophore contains a very large number of embryos in
various stages of development. Its proximal part is cylindrical
and lies in the body-cavity of that part of the fertile individual
which was developed before the more distal part of the same
individual took on the external characters of an ovicell. The more
distal part of the embryophore divides into several more or less
cylindrical lobes, which radiate out into the parts of the ovicell
lymg between the oblique series of zocecia. I have convinced
myself that the “secondary embryos” arise by a process of em-
bryonic fission; but I propose to withhold the details of this
process for a later paper, in which I hope also to discuss certain
brown vesicles, occurring in the ovicells, polypide-buds, tentacles
and elsewhere, which retain their colour even in paraffin-sections,
and are hence an excessively conspicuous feature in preparations
of this species.
The general results of this series of observations are as
follows :—
(1) the normal occurrence of embryonic fission in Cyclo-
stomata is confirmed by the examination of a new case ;
(2) the ovicell of Idmonea serpens is shown to be a modified
zocecium, and its early history is indicated ;
(3) certain considerations suggest themselves with regard
to the classification of the Cyclostomata.
1 See Quart. J. Micr. Sci. xxx1x. p. 94.
|
210 Mr Harmer, On Cyclostomatous Polyzoa. [Oct. 26,
I am the more inclined to consider the last point because of
the views which have just been expressed by Dr Gregory?, who
reluctantly accepts the conclusions that “ there are no true geneta
among Cyclostomata, but only certain convenient, but artificial,
groups of species”; that “there is no hope in this order of ever
establishing divisions with the same absolute diagnoses as in
most other groups of Invertebrates”; and that “ Zoarial characters
are the only ones available for systematic work among the Cyclo-
stomata.” Dr Gregory’s classification is based mainly on the
characters of the entire colony and of the zocecia. It appears to
me that he has omitted to notice sufficiently a most important
adjunct to classification, namely the ovicells, whose value in classi-
fication has previously been insisted on by Waters? and myself.
I fully admit the difficulty of distinguishing genera and species
among the Cyclostomata, and I by no means assert that it is
always possible to determine the species to which a fragment of a
Cyclostome, or even a single colony belongs. The ovicells, which
appear to me to form the surest diagnostic features, are unfortu-
nately not always available; and on the assumption that they are
‘modified zocecia there was probably a period in the evolution of
the group during which the fertile zocecia were not to be dis-
tinguished externally from the others. But it appears to me that
in dealing with recent species at least, the study of a large series
of specimens, in various stages of their existence, and particularly
during their reproductive period, enables us to establish “absolute
diagnoses” which are in no way different from those which dis-
tinguish the members of other groups of Invertebrata. It may
not always be possible to apply these diagnoses in a particular
case, but I think that it would be going too far to assert that the
differences do not exist.
In spite of the agreement of Crisia, Idmonea and Lichenopora,
the three genera which I have specially studied, in the fundamental
fact of the occurrence of embryonic fission, the details of their
development and particularly the structure of the ovicells and of
the embryophores are widely different in the three cases. This I
shall hope to show, in greater detail, in a future paper. It is true
that these are extreme cases; but the differences are not confined
to extreme cases, as the following instances will show.
I have on a previous occasion attempted to show that the British
species of Crisia can be distinguished from one another by their
ovicells*. Another genus in which the diagnostic value of the
1 J. W. Gregory, ‘‘ Catalogue of the Fossil Bryozoa in the Department of Geology,
British Museum.” 8vo. 1896, p. 21.
2 Mr Waters has returned to this point, in a review of Dr Gregory’s Catalogue
published in the November number of Natural Science (Vol. 1x. 1896, p. 334).
3 Quart. J. Micr. Sci. xxxu. 1891, p. 127.
1896.] Mr Harmer, On Cyclostomatous Polyzoa. 211
characters of the ovicells is very apparent is Hornera; but without
going further into this case, I may be permitted to compare three
recent species of Dvuastopora (Berenicea in Dr Gregory’s sense)
which I have examined with the special object of testing Dr
Gregory's views. In each case I have succeeded in observing the
continuity of the ovicell with a cylindrical portion situated in the
ordinary series of zocecia and representing the condition in which
the ovicell occurred before it took on the external characters of an
ovicell. This condition was in Jdmonea serpens shown to be
associated with the fact that the ovicell is a modified zocecium,
and I have little doubt that the same conclusion may be drawn
with regard to Diastopora. I wish to insist on this point because
Dr Gregory has figured ovicells, in various species of Berenicea,
which from my examination of recent genera I have no hesitation
in regarding as modified zocecia (cf. Pl. 101, fig. 3; Pl. Iv., figs. 1, 2,
5, 6 of his Catalogue). These he terms “ gonocysts,” and on p. 12
he defines a gonocyst as “ A form of marsupial chamber produced
by expansions within the zoarium, and not by the modification
of a single zocecium.” I believe, on the contrary, that the ovicell
is probably a modified zocecium in all Cyclostomata. This is
certainly true of Crisia, Idmonea serpens and Lichenopora.
In Diastopora suborbicularis, Hincks, the fertile zocecium is
but slightly expanded distally, as in Dr Gregory’s Pl. Im1., fig. 3.
In D. obelia, Johnst., the dilated part of the ovicell is very much
more developed, while in D. patina, Lamk., the dilated part grows
out laterally on each side in a direction concentric with the margin
of the colony. The lateral growth may be so marked that the
dilated part of the ovicell grows completely round the discoidal
colony, and with the secondary union of the two lobes of the fan-
shaped colony, the two lobes of the ovicell may also meet one
another and form a complete ring-shaped ovicell. Should a second
ovicell be developed as a modification of a younger zocecium than
that which produced the first one, it is developed concentrically
with the first and of course outside it.
The specific difference between D. suborbicularis and D. patina
is further expressed in the slight development and vertical position
of the “terminal membrane”’* in the former, and its large develop-
ment, and oblique position (owing to the great extent of the basal
lamina) in the latter; and in the fact that the fan-shaped form of
the colony is developed into a secondarily discoidal form much
earlier in D. patina than in D. suborbicularis.
These examples will serve to show that recent species of
Cyclostomata may be distinguished by means of their ovicells. It
will further be apparent that the ovicells themselves belong to
1 Quart. Journ. Micr. Sci. Xxx1x., p. 93.
212 Mr Harmer, On Cyclostomatous Polyzoa. [Oct. 26,
several distinct types. Thus the ovicell of Crisia is practically
a zocecium which has become pear-shaped. Its morphological
value as a modified zocecium is apparent at the first glance owing
to the fact that it replaces an ordinary zocecium in the alternate,
biserial arrangement characteristic of this genus. There is no
sudden constriction between the proximal and the distal part of
the ovicell; and this condition is probably due to the fact that as
the fertile polypide is never more than a mere bud, the proximal
part of the ovicell at no period functions as an ordinary zocecium.
In other Cyclostomes which I have examined, there is a sudden
enlargement of the ovicell which corresponds with the point at
which it becomes, so to speak, disengaged from the series of zocecia.
This enlargement no doubt corresponds with the time at which
the embryophore begins to increase rapidly in size.
In the Tubuliporidae, the ovicell in other respects resembles
that of Crisia, except that it projects less beyond the ordinary
zocecia. In the simpler cases, as in Diastopora suborbicularis, it
is still more or less pear-shaped, but im other species of the same
genus and in Jdmonea serpens it enlarges so as to grow round the
neighbouring zocecia. The lobes of the ovicell then unite with
one another on the distal side of the zocecium round which they
have grown, and the zocecium is left as a column passing freely
through the cavity of the ovicell.
The ovicells of Hornera probably form a third type; while
those of Lichenopora are the most complicated which I have so far
examined. Here the ovicell no longer develops as a continuous
cavity; but, although at its commencement it is merely an ordinary
zocecilum, its extent is afterwards increased by the fusion with it
of the “alveoli” which are developed at the growing margin of the
colony.
I hope to have the opportunity of making a more extended
study of the ovicells in this group of Polyzoa; but in the mean-
time I wish to emphasize my opinion that it will probably not be
found impossible to give diagnoses of recent Cyclostomatous genera
with much less precision than those which are given for the genera
belonging to other groups of Invertebrates.
Certain considerations with regard to the general architecture
of the Cyclostome colony have suggested themselves to me during
my recent observations’.
The colony in Lichenopora is a modified funnel, whose mouth
1 The varieties of form assumed by the colony, in various genera and species of
Cyclostomata, strikingly resemble those which have been described by Mr H. M.
Bernard in the Coral Turbinaria (‘*Notes, Morphological and Systematic, on the
Madreporarian Genus Turbinaria,” Ann. Mag. Nat. Hist. (6) xv. 1895, p. 499;
‘“Catalogue of the Madreporarian Corals in the British Museum” (4to.) Vol. 11. 1896).
It is not unlikely that the growth of a colony of Polyzoa may be regulated by laws
which resemble those that govern the growth of a colony of Zoantharia.
1896.] Mr Harmer, On Cyclostomatous Polyzoa. 213
has expanded widely so as to cover the proximal part of the colony
and thus to give rise to the discoidal form characteristic of the
adult*. The mouth of the young funnel is closed by the uncalcified
“terminal membrane.” This, during the growth of the colony,
gives rise to zocecia in such a way that a part of it, capable of
forming new zocecia, is left round the entire circumference of the
colony, in addition to the part which appears to cover the entire
upper surface, and from which the “cancelli” are developed. In
Iachenopora the adult colony assumes the form of a somewhat
modified funnel, but in Flosculipora pygmaea, MacGill., an Aus-
tralian species, the funnel-shaped form persists with practically no
modification.
The peculiarities of Lichenopora are thus partly dependent on
the mode of development of the terminal membrane, which forms
an uninterrupted, annular margin round the mature zocecia and
ovicell.
In another series of forms, including Jdmonea serpens, Tubuli-
pora and Diastopora, the proximal part of the terminal membrane
is used up completely in the formation of the proximal zocecia.
The terminal membrane thus becomes incomplete on the proximal
side of the colony, but it remains as a more or less semicircular
margin, capable of giving rise to new zocecia, on the distal side.
Growth thus ceases on the proximal side, and the colony assumes
a fan-like instead of a circular shape. The terminal membrane is
commonly used up in the formation of zocecia at a point opposite
the primitive disc of the colony, and the growing margin is thus
divided into two. By further growth of these parts, accompanied
by a cessation of growth in the middle of the distal side of the
colony, the fan becomes bilobed; and by further subdivisions of
the parts of the terminal membrane, each lobe becomes further
lobed. This interruption and subdivision of the terminal mem-
brane is one of the essential differences between Lichenopora and
Idmonea, and it is a noteworthy fact that this generic distinction
is already marked at the commencement of the life of the colony.
I do not at the present moment include the branching species of
Idmonea in this comparison ; and it is possible that the affinities
of I. serpens are really with species of Tubulipora, as many authors
have assumed by placing it im that genus, rather than with forms
like J. atlantica, I. radians and other similar species.
In recent species of Diastopora, the colony early acquires a fan-
like shape. The terminal membrane does not, however, divide,
and the colony does not assume a lobed form. It is well known
that in this genus the two lateral edges of the fan grow towards
the proximal end of the colony, where they unite secondarily with
1 Quart. Journ. Micr, Sci. xxx1x., pp, 81, 93.
214 Mr Harmer, On Cyclostomatous Polyzoa. [Oct. 26,
one another. In other words, the two free ends of the interrupted
terminal membrane grow towards one another above the proximal
end of the colony. When they have united, complete fusion takes
place, and the two halves of the membrane become completely
confluent. This results in the assumption of a secondarily discoidal
condition, which differs fundamentally im origin from the discoidal
colony of Lichenopora, where the entire rim of the colony is a
direct derivative of the rim of the young funnel-shaped stage.
In Crisia again, the branching colony is produced by the
repeated division of the terminal membrane, accompanied by great
elongation of the lobes or branches to which the growing-points,
or segments of the terminal membrane, give rise. The branches
at the same time become jointed. In other words, a Crisia-colony
is comparable with a funnel whose distal end has become repeatedly
divided in a longitudinal direction, the divisions extending a
varying distance towards the base of the colony. The basal lamina
of Lichenopora and Idmonea is thus represented by the “backs” of
the branches.
The above instances will serve to show that the zoarial form of
several types of apparently dissimilar Cyclostomes is regulated by
a law of growth which is probably common to the majority of
recent species, if not to all. The unilaminate condition of Hornera,
of Frondipora verrucosa, and of erect species of [dmonea is readily
intelligible on the supposition that the “backs” of the branches
correspond with the basal lamina of encrusting species.
1896.] Prof. Stokes, On the Nature of the Réntgen Rays. 215
Monday, 9 November, 1896.
Mr F. DARWIN, PRESIDENT, IN THE CHAIR.
The following were elected Associates of the Society :—
Mr A. E. Smith, Cambridge.
Dr Novak, Prag.
Mr J. Henry, Trinity College.
Mr W. C. Henderson, Trinity College.
Mr G. B. Bryan, St John’s College.
The following Communications were made to the Society:—
(1) On the Nature of the Réntgen Rays. By Professor Sir
G. G. STOKEs.
In this communication the author explained the views he had
been led to entertain as to the nature of the Rontgen rays, and
to a certain extent the considerations which had led him to those
conclusions. As Rontgen himself pointed out, the X rays have
their origin in the portion of the wall of the Crookes tube on
which the so-called cathodic rays fall, and it is natural that our
notions as to the nature of the X rays should be intimately bound
up with those we entertain as to the nature of the cathodic rays.
Two different views have been adopted on this question. Several
eminent German physicists hold that the cathodic rays are essen-
tially a process going on in the ether, the nature of which nobody
has been able to explain; and that if any propulsion of molecules
from the cathode accompanies them, it is merely a secondary
phenomenon. The other view is that the cathodic rays are not
proper rays at all, but that they are essentially streams of mole-
cules. The latter view is that which, so far as the author knows,
is universally adopted in this country. The author expressed the
fullest conviction that the cathodic rays are no mere process going
on in the ether, but that the propulsion of molecules is of the
very essence of the phenomenon; only it is to be remembered
that the molecules are not to be thought of as acting merely
dynamically, by virtue of their mass and velocity; they are
carriers of electricity; and it would seem to be mainly to this
circumstance that some at least of their effects are due. He
indicated what he believed to be the true answers to the objections
of those who regard the cathodic rays as processes in the ether ;
and adopting the theory that they are streams of molecules ex-
plained how, in his opinion, this theory, taken in connection with
the more salient features of the X rays to which the cathodic
rays give birth, leads us to a theory of the nature of the X rays.
216 Prof. Stokes, On the Nature of the Réntgen Rays. [Nov. 9,
Everything leads us to regard the X rays as being, like rays
of light, some process going on in the ether, and sufficient imdica-
tions of their polarization appear to have been obtained to lead
us, at least when those indications are taken along with the
undoubted polarization of the Becquerel rays with which they
have so many properties in common, to refer the Rontgen as well
as the Becquerel rays to a disturbance transverse to the direction
of propagation. The absence of refraction, which is so remarkable
a feature of the X rays, leads us to regard their progress through
ponderable matter as taking place by vibrations in the ether
existing in the interstices between the ponderable molecules; a
view which if correct leads us incidentally to a somewhat novel
view as to the mechanism of the refraction of light. The absence,
or almost complete absence, of diffraction and interference of the
X rays leads to one of two alternatives :—either that they are of
excessively short wave length, or that they are non-periodic or
only very slightly periodic, the X light being on the latter sup-
position regarded as a vast succession of independent pulses
analogous to the “hedge-fire” of a regiment of soldiers. According
to the author’s view, each electrically charged molecule on arrival
at the target gives rise to an independent pulse, and the vastness
of the number of pulses depends on the vastness of the number
of molecules in even a minute portion of ponderable matter.
(2) On the Contact Relations of certain Systems of Curcles
and Conics. By Mr W. McF. Orr.
_[This paper will appear in Transactions, Vol. xvi. Part IT.]
(8) On certain cases of Discharge in Vacuo and on the zigzag
path of Lightning. By J. Monckman, D.Sc., Downing College.
Prof. J. J. Thomson, when conducting a series of experiments
on the striation of sparks in vacuum tubes, made use of various
forms of tubes, among which was one which may be called a
multiple are. It consisted of a rectangular tube with two short |
ones containing the electrodes (Fig. 1). The two sides CAH
and GFD were exactly equal in length. When a discharge took
place through the tube, it was observed that at a low pressure the
spark passed down one side and on changing the direction of the
current, the spark passed down the other side, continuing to change
sides on each reversal.
In order to avoid repetition I will speak of this changing of the
spark from one limb to another, when the direction of the current
is changed, as the ‘ Reversal of the Spark.’
1896.] Mr Monckman, Discharge in Vacuo, ete. bal ki
The multiple arc tube A was jomed to a mercury gauge B
and onward through the clip H to the receiver of a mercury
pump. By this arrangement the pressure may be regulated to the
Bre. a;
greatest nicety by keeping the receiver exhausted and carefully
opening H, a little air may be drawn out. And with a little
practice there is no difficulty in going through a whole series of
readings varying two or three millimetres at a time.
The first series of experiments were tried with ordinary air,
and it was found that when the pressure was reduced to 19 mm. the
reversal of the spark commenced, but it ceased when the pressure
fell to 11 mm., beyond which the spark passed down one side only.
Change of gases. I next tried the effect of changing the gas,
and found that only one refused to produce any reversal while
another acted very poorly, all the other gases giving reversals at
pressures varying with the nature of the gas used.
Very great care was exercised in preparing pure and dry N, H,
and O, the object being to test whether a pure dry elementary gas
would produce the phenomenon; also pure N was mixed with HCl
(pure) with what result will appear in the table following.
It is interesting to notice that the two gases that produce the
least effect are those that were found by Faraday to give the worst
examples of brush discharge.
Density of spark. There is a particular density of spark more
favourable than others for producing the reversal. The most
convenient adjustment of the vibrating contact breaker of the coil
can be found only by trial, as it varies with the coil used and with
the tube. I found that a position about half-way between the
position of brightest spark and that at which the hammer vibrated
with frequent stoppages, answered very well with the particular
instruments used. The proper density appears to be as small a
discharge as can be got to pass steadily, since a dense one bursts
through and often passes down both sides at once.
Variation of the electrodes. In the experiments described the
electrodes were platinum wires, on the ends of which small knobs
WOL; 1X. PT“. 176
218 Mr Monckman, Discharge in Vacuo [Nov. 9,
had been fused by exposing them to the heat of the electric are.
With some of the gases other electrodes were used and it was
found that Pt, in all forms, Pd, and C, were effective, while Al
was only slightly so. The former bodies occlude gases, and when
the pressure is reduced, drive off small particles of their substance
into the surrounding space, while Aluminium does not do so.
I have collected into one table the results obtaimed by the
previously described experiments.
Table shewing the changes produced by variation of
electrodes, of gases, and of pressure.
Pressure in | Pressure at Pressure at
mm. at which |} which it goes which it passes
Electrodes Gas the spark down both down one side
reverses sides only
Platinum | Air 19 to 11 10 |
wire with | (ordinary) 17 to 9 | 18withvery 8
small knobs 19 to 11 strong 10
at the Carbonic 18 to 11 currents
ends dioxide 23 to uit 10
28 to 10
Ammonia 18 to 8t a
gas 25 to 11 10
22 to 8 7
30
Ether 38 ?
Coal gas 30 to 11 10
Hydrogen 30 to 8 8
Oxygen 27 to 14 14 to 5 4 Reversals poor
Hydrochloric
acid gas none none all pressures
Nitrogen 14 to 8
Mixed Gas : se
HCl and N BS 0 e é
Platinum
foil Air 36 to 16 6
Paladium | Air 35 to 20 10
Nitrogen 30 to 25 10
Carbon Ammonia gas| 50 to 20 19
Aluminium very little
indeed |
+ When the sparks were not passed until the pressure was reduced to 30m.,
they were greenish and reversals were obtained. When the sparks were passed as
the pressure varied, the greenish colour soon disappeared and reversals occurred at
from 18 to 25m. pressure.
* After using HCl and N the electrodes became covered with a brown substance
and the reversals ceased to appear although trial was made with dry and damp air
and alcohol vapour, but they were again obtained after heating the platinum in the
blow-pipe flame.
Further experiments showed this to arise from the Hydrochloric acid gas which
not only gave no reversal itself, but so acted upon the platinum as to prevent
reversal with other gases. The same action took place in a small degree with
Oxygen, which caused the reversal to fail in Hydrogen the first time after Oxygen
had been used,
1896.} and on the zigzag path of Lightning. 219
Position of the electrodes, Angle of the short tubes and Occluded
Gases. When the short tubes containing the electrodes were fixed
obliquely, it was found that the spark passed along the limb
which allowed the negative current the more direct course into
the main tube.
This took place with all gases, including Oxygen and Hydro-
chloric acid, which had no effect in the preceding experiments.
When however the knobs were pushed forward, the old form
of reversal was obtained, Oxygen giving poor results and Hydro-
chloric acid none at all.
Since reversals were obtained with electrodes that occluded
gases and not with Aluminium, it was of interest to try by
experiment whether such gases produced any part of the effect.
Three platinum wires with knobs at the ends were fixed to an
ebonite rod. The distance between the first and second was
exactly the same as that between the second and third. The first
and third were joined together, the whole placed under a receiver
and exhausted. Afterwards Hydrogen was liberated electro-
lytically upon No. 1 and Oxygen upon No. 3, but on replacing
and exhausting no difference could be detected.
Charging of the tube. Supposing that it was possible that the
glass tube might become charged and so influence the spark, I
tried the effect of increasing such charge by placing strips of
metal under one limb of the tube and found that the discharge
was drawn down the side on which the metal was placed.
By using two pieces of metal, or two small saddles of lead
joined by a wire, and placing one at C (Fig. 1) and the other at D,
or one at # and the other at G,I found that the spark could be
made to pass down either side and to reverse when the current
was changed. The direction being from the negative electrode
past the nearest saddle. Thus if the negative were on the right
hand and the saddles at # and G, the spark passed along the limb
A and on reversing along the limb F, but if the saddles were at D
and C it passed through F and reversed through A.
We could thus produce the reversals as we wished and part of
the original phenomenon was explained. To determine how much,
two other pieces of apparatus were tried, but as both methods
gave the same results I will describe one only.
A jar 6 inches in diameter and 8 inches in height was placed
upon a metal plate and made tight with soft wax. The two lower
electrodes A and B were in metallic communication with the
plate, the upper ones C and D were connected together outside of
the jar. D was fused into a glass tube which could be moved,
backward or forward, in order to make the distances exactly equal
(3 inches).
Reversals were observed between the pressures 45 mm. and
li
220 Mr Monckman, Discharge in Vacuo [Nov. 9,
25 mm. beyond which the current always took one path and could
not be changed.
Innes BD,
With this jar reversals were obtained not only when the
current was reversed, but also on restarting after a short break.
The latter appeared to be caused by an agency about half as
energetic as the former.
After allowing air to enter the receiver and again exhausting,
the force that previously acted was found to have decreased, and
the next discharge might or might not take the same path as the
last before admitting the air.
When using a powerful Wimshurst machine, in a dark room,
during the performance of an experiment to be described later, I
observed that when the knobs were opened beyond the position of
taking an ordinary spark, there began to be a glow around the
negative which illuminated a somewhat globular space around
that pole. The positive spark passed into this space, but con-
stantly changed its course, sweeping the negative charge away
from its path, it then took another path and having cleared that
of negative changed again and so on through a kind of cycle.
If there were two paths open as Fig. 2 and a spark passed
from C to A, removing part of the glow from the space around A,
there would (after cooling) be a greater tendency for the next
spark to pass between D and B.
On the other hand if after a spark had passed between C and
A the direction of the spark were reversed, it would most probably
pass from B to D, there being a larger quantity of negative around
D than around A.
This is probably the explanation of the previous reversals and
also why the introduction of air into the receiver decreased the
power of producing it.
Underlying the whole matter is the cause of the production of
the glow at the negative and why some gases produce it better
1896.] and on the zigzag path of Lightning. papel
than others; on these points my experiments do not enable me to
offer any opinion.
Zigzag form of spark. When the path of a discharge is long,
the spark passes in the well-known zigzag course, often giving off
at the angles a series of side flashes or ramifications. This is
usually explained by supposing that “The spark finds this form
of path easier owing to the presence of irregularly distributed
particles of dust which act as stepping-stones, giving the discharge
a path of less resistance although longer.”
The action of the strips of metal in the previously described
experiments led me to think that the irregular form of the path
was due to particles charged by induction, attracting (not con-
ducting) the spark away from the straight line and the ramifica-
tions were discharges to these particles, after which the spark was
free to return to its natural course.
In order to test the correctness of this idea I first fixed a
number of small pieces of tinfoil upon a piece of mica by means of
shellac varnish, and this upon an ebonite rod. When the stream
of electricity was passing between the poles of a Wimshurst
Machine, the mica disc was placed a little to one side of the path.
The sparks were drawn out towards the disc.
In order to obtain the ramifications at the angles I placed a
large number of small brass beads upon silk threads about one
millimetre apart. These threads were then fixed to an ebonite
stand in parallel lines and as close together as could be managed
without allowing them to touch. When this was placed on one
side of a straight spark, the path immediately changed, forming
an angle towards the beads, and giving off the peculiar ramifica-
tions that are so often seen in photographs of lightning.
The action of charged dust, &. passing away from the nega-
tively charged conductor will no doubt produce part of this,
especially when the spark is short, but in the case of lightning I
believe the inductive action to be much more important.
222 Messrs Heycock and Neville, [Nov. 23,
Monday, 23 November, 1896.
Mr F. DARWIN, PRESIDENT, IN THE CHAIR.
The following were elected Fellows of the Society :
H. M. Macdonald, M.A., Fellow of Clare College.
G. H. J. Hurst, M.A., Fellow of King’s College.
The following Communications were made to the Society :—
(1) On the Superficial Colour of a Silver-Zinc Alloy. By
C. T. Heycocx, M.A., King’s College, and F. H. NEviixe, M.A.,
Sidney Sussex College.
Whilst granulating by pouring into water an alloy of silver
and zinc whose composition was very nearly AgZn (62°25 °/, Ag)
we found that it was superficially coloured a red tint closely re-
sembling that of copper although before melting it was silvery
white. The only reference we can find in the text books is in
Percy's Metallurgy where it is stated that some alloys of silver
and zine acquire a pale pink tinge on exposure to air. A variation
in the composition of the alloy to the extent of 5 per cent. of
silver more or less does not much impair the colour, but with a
deviation from AgZn of 10 per cent. of silver the effect is no
longer noticed.
The present communication contains the results of some ex-
periments we have made on this coloration. There appear to be
two methods probably not radically different of turning the silver
white alloy into the red state. The best way is to heat the alloy
up to a temperature near 300°C., 285° is the lowest effective
temperature, and suddenly to chill it. In this way 1t acquires a
fine red colour, provided that the cooling has been rapid. The
necessity for rapid cooling is connected with the fact that if the
red alloy is heated to 150° C. it turns white. It thus appears
that the red colour is due to a substance which cannot exist above
150°, and which cannot come into existence unless the body be
heated to 300° C.
These peculiar conditions distinguish the phenomenon from all
superficial colour changes of metals known to us.
We found that the cooling could be effected by letting filmgs
of the alloy fall through the air or by throwing the hot metal into
water, alcohol, benzene or ragosine. As the last two liquids con-
tain no oxygen it became doubtful whether the presence of oxygen
was indispensable for the effect. We made numerous experiments
to settle this poimt, the most conclusive bemg the formation of
1896.] On the Superficial Colour of a Silver-Zinc Alloy. 223
the red colour in an atmosphere of pure hydrogen. To effect this
some filings of the alloy were placed in a glass tube about 18”
long. Pure dry hydrogen was then passed through the tube for
an hour or more, the tube being heated throughout its length to
at least 300° C. The tube was finally sealed by the blow-pipe at
both ends, the arrangements throughout being such that no air
could possibly enter the tube containing the alloy. To avoid the
danger of the hydrogen containing oxygen it was prepared, in one
experiment from palladium which had been charged at a lower
temperature, and in another experiment, the hydrogen, from zine
and sulphuric acid, was passed through a foot of red-hot copper
gauze before entering the alloy tube. All important joints were
made by sealing the glass tubes to one another with the blow-pipe.
We thus obtained two closed tubes containing a little of the
alloy in an atmosphere presumably free from oxygen. The alloy
in the tube was then brought to one end and that end heated to
300°C. while the other end was cold. We then threw the hot
alloy to the cold end of the tube and shook it there to promote
rapid cooling. In both cases it turned red. We have also obtained
the red in an atmosphere of carbon dioxide.
Hence the formation of the red colour does not depend on the
chemical nature of the surrounding atmosphere: it ts a change
for which the alloy ws itself sufficeent. We find that in a low
vacuum of anything above a millimetre the red comes as easily
as in air, but Mr Skinner, who was kind enough to get a good
vacuum, say *,mm. in a tube of the alloy, found that it did not
change colour. We have since verified this repeatedly but we
find that if such a high vacuum-tube be heated above the
temperature at which it was sealed the red can be obtained in it.
The behaviour of these vacuous tubes is explained we think by
Mr Skinner's suggestion that it is due to variations in the power
of cooling by convection. In low vacua the convection cooling of
the particles of alloy by the gases in the tube will be almost as
rapid as at the atmospheric pressure, but in high vacua this mode
of cooling will be absent and hence the alloy cools too slowly to
turn red. If we heat such a tube to a higher temperature gas
is given off from the walls and the vacuum falls, hence the red
can be obtained.
The other way of getting the red colour is to turn up in a
lathe or to file the white alloy. The fine particles thus obtained
have a pink tinge, but in the course of a few days or weeks they
become a bright pink. This gradual change is not as one might
think due to the air but to a latent power communicated to the
turmings as they are separated from the main mass of metal
the temperature of each fragment being very high at the moment
of its separation.
224 Messrs Heycock and Neville, Superficial Colour, etc. [Nov. 23,
That the air has nothing to do with this gradual change of
colour can be proved by heating some of the turnings to 150° C.
and then exposing them to the air. A month’s exposure gives
no trace of red. In fact, provided the alloy has been annealed at
150°, the white colour is quite stable in air, In moisture or in
oxygen.
The red colour also seems to be quite stable at ordinary tem-
peratures. The red resists dilute sulphuric and hydrochloric acids
and the alkalies, and what is more remarkable, it is not affected
by sulphuretted hydrogen or by ammonium sulphide reagents
which blacken silver. The action of ozone on the red is very
slow but it does finally blacken the alloy.
These are the main facts we have observed. We do not know
the chemical change associated with the red colour, and on account
of its being a surface action involving minute quantities of matter
it will probably be very difficult to settle this. Oxygen may play
a part in the reaction, for there is almost certainly some zinc oxide
in the alloy, and possibly some oxygen occluded by the silver.
The upper limit of temperature 300° is that at which Ag,O is
completely decomposed under atmospheric pressure.
We hope however to be able to replace speculation by facts in
a further communication.
(Note added Dec. 31, 1896.)
Since reading the above paper before the Society, we have
prepared some of the alloy from metals that had previously been
scrupulously freed from oxygen or oxides, the silver by heating to
a red heat for some hours in an atmosphere of hydrogen, and the
zine by distillation in a hydrogen vacuum. The alloy made in
hydrogen from metals thus prepared turns a fine red when heated
and suddenly cooled in the unopened sealed tube in which it was
made. The colour change cannot therefore be due to oxygen or
to the formation or decomposition of oxides.
We have also found that a silver-cadmium alloy AgCd under-
goes somewhat similar colour changes.
(2) Note on Thermometric “Fined Points. By Haye
GRIFFITHS, M.A., Sidney Sussex College.
It is commonly assumed that our present definitions of the
thermometric fixed points are theoretically sound and in practice
satisfactory. This may possibly be the case, but, at the same time,
there are certain ambiguities having their origin in experimental
difficulties which may render profitable a consideration of the whole
matter; especially as recent advances in the science of exact
thermometry make it impossible to tolerate any doubt as to the
fundamental definitions on which that science depends.
1896.] Mr Griffiths, On Thermometric “Fixed Points.” 225
SecTION I. Freezing Point.
I assume that the ordinary definition of freezing pomt is as
follows: “the temperature of a mixture of ice and water when the
temperature condition is one of statical equilibrium.”
From the theoretical point of view there appear to be no objec-
tions to offer to this definition; practically, however, it is found
unsatisfactory.
As Nernst has pointed out, no such statical condition is possible
if the exterior temperature differs from that of the mixture, or if
heat is supplied by the stirring, We. Now, under the ordinary
conditions of a laboratory the surrounding temperature is very
different from that of the mixture, and although it may be urged
that the convergence temperature t, closely approximates to the
true freezing point t, when the masses of ice and water are con-
siderable, the difference is nevertheless a measurable one, and when
such is the case we cannot be said to possess an ideal standard.
In other words, in practice the system is a dynamical, not a
statical one.
The method of under-cooling and super-fusion does not, as
Nernst has shown, suffice to overcome the difficulty, and some
recent observations of my own lead to the conclusion that very
accurate results can only be looked for when the condition is truly
statical.
Another practical difticulty is the inevitable question as to the
purity of the material. I take it that the definition assumes abso-
lute purity, otherwise the temperature would not be fixed. The
work already accomplished by Loomis, Jones, Abegg, Wildermann,
Harker and others has sufficiently proved how considerable are
the effects of small impurities; on the other hand, we certainly do
not as yet know (and it appears to me improbable that we ever
shall know) the true freezing point of pure water, thus, if we are
compelled to wait for that knowledge before we decide upon
the value of our lower fixed point there is little prospect of
finality.
As an illustration. At the Liverpool meeting of the British
Association I communicated the results of some recent experi-
ments which, to my regret, forced upon me the conclusion that
the depression of the freezing point due to the solubility of
glass was greater than had hitherto been supposed. It is
probable that the difficulties which have been encountered by
enquirers into the freezing point of dilute solutions have been
partly due to want of attention to this matter, for I can find no
record of experiments in which the water used has been from
the time of distillation uncontaminated by contact with glass.
This would be of small consequence if the depression thus
226 Mr Griffiths, On Thermometric “Fixed Points.’ [Nov. 23,
caused was always constant; but glass varies greatly in composi-
tion and its solubility probably depends so largely on the nature
of the substances previously in solution that the effects may be
very variable. We should thus be compelled to use platinum or
gold vessels, and the heavy expense entailed would alone suffice to
put the freezing point of “pure water” out of court for all prac-
tical purposes. Granted that these difficulties could be overcome
there arises a question as to the influence of the contained gases.
Assuming the accuracy of the ordinarily-accepted constants we
find that the freezing point of water if saturated with oxygen
and nitrogen would be lowered about 0°:002 C., and it is difficult
to see how this cause of error is to be eliminated. Under such
circumstances the experimenter who diminishes the causes of error
only departs the further from what we may call the practically
accepted standard, and additional refinements may but introduce
greater confusion unless some general agreement 1s arrived at.
An observer who is in the habit of standardising thermometers
usually repeats his experiments under similar conditions, and find-
ing his results consistent in themselves is apt to conclude that his
standard is identical with that of others.
The following is an illustration of the danger arising from such
a conclusion.
I have been in the habit of standardismg my own platinum
thermometers by immersing them in a large copper vessel contain-
ing about 15 lbs. of finely-powdered ice and ordinary distilled
water. ‘This vessel is separated from a second copper one by a
layer of Norwegian felt nearly 2 inches in thickness. The thermo-
meters are immersed to a depth of 8 or 10 inches, and, where they
pass into the vessel, are surrounded by felt. The indications of
these thermometers are unaffected by the stem temperature, and
under these circumstances it appeared probable that the tempera-
ture indicated could not be appreciably affected by the temperature
of the laboratory. I have recently been using a platinum thermo-
meter presenting certain novel features which I believe tend to
greater accuracy, also the coils of the resistance-box consist of
naked wires immersed in rapidly- stirred oil, and thus the great
impediment to accurate work, viz. uncertainty as to the tempera-
ture of the box coils, is alinaraniedl On four different occasions
this thermometer was placed in the ice, as above described, and its
resistance on these respective occasions was as follows :
1293968
‘966
‘963
‘966
Ba CT ere calles me
Now in this thermometer the value of —- (at 0°) = 5-073, and
dt
1896.] Mr Griffiths, On Thermometric “Fixed Points.” 227
thus a difference of 5 in the last figure represents a change of
0°001, hence the greatest difference from the mean on these
occasions was considerably less than 1/100U°. This at first sight
appeared satisfactory.
At the commencement of October I was enabled to make a
couple of determinations of the freezing point with the same
thermometer in a new apparatus which has been constructed for
the purposes of an investigation into the freezing point of dilute
solutions. This apparatus (the particulars of which I hope subse-
quently to publish) has been so devised that the temperature of
the air space surrounding the entire vessel (as also that of the
walls surrounding that air space) is at the temperature of the
mixture in the inner vessel. I have only as yet been able to make
two determinations; the results are as follows:
1293-947
‘948
Hence it would appear that in spite of the agreement in the
previous results, the influence of the room temperature was
sufficient to cause a rise exceeding 0°005 in the temperature.
The similarity of the conditions throughout the first series accounts
for the agreement amongst their results.
It may be objected that such accuracy is unnecessary. ‘T’o
this I would reply that it is evidently desirable that the limit of
error of a “fixed point” should certainly be less than the limit of
experimental error due to the instruments by which temperature
can be measured.
I do not feel in a position to make any satisfactory suggestion ;
at the same time I think we should be moving in the nght
direction if we more strictly defined the conditions of a deter-
mination. For example, we should obtain more constant results
than are possible under existing circumstances if we adopted, as a
temporary standard, water distilled at a certain rate from alkaline
permanganate within some definite but convenient limit of time,
which, having been collected in either copper or Jena glass
vessels was then mixed in certain definite proportions with ice,
crystallised from it, and placed in a vessel of definite size when
the temperature of the laboratory was within certain limits*.
The ideal standard being experimentally unobtainable, we require
a practical one if uniformity and accuracy are to be attained.
* As a difference in pressure of 100 mm. causes a change of about 0°-001 in the
freezing point, a statement as to the standard pressure should (in anticipation of
further advances in thermometry) be added to any definition such as that suggested
supra.
228 Mr Griffiths, On Thermometric “Fixed Points.” [Nov. 23,
SecTION II. Boiling Point.
The following is, I believe, our definition of standard boiling
point: “the temperature of the steam issuing from water boiling
under a pressure of 760 mm. of mercury at temperature 0° and at
sea-level 45°.”
From a practical point of view this definition is, I now
believe, sufficient. Until recently I have been doubtful as to the
rapidity with which, if the barometer changes, the steam acquires
the temperature corresponding to the new pressure, and I anti-
cipated that experiment would show there was a considerable lag.
I had hitherto failed to satisfy myself on this pomt since the un-
certainty arising from want of knowledge as to the actual tem-
perature of the box coils was greater than the temperature
changes consequent on the changes of pressure usually occurring
during an experiment, and results obtained from observation on
different dates would convey no information concerning the lag, if
any. As previously indicated, I now can measure the changes in
temperature of the box coils (I do not here refer to the absolute
temperature) certainly to within 0°01 C., and the resulting observa-
tions are sufficient to settle this lag question, at all events to my
own satisfaction. On October 7th Mr Whetham and I were
engaged in standardising a thermometer for the purposes of a
joint investigation. The pressure on this occasion proved to be
so variable that it appeared hopeless to attempt an accurate deter-
mination of the resistance at 100°. We, however, continued the
observations for a period of nearly 3 hours in the hope of throw-
ing some light on the matter to ae I have referred. The
results are shown in the following table, but are much better
exhibited when plotted. The actual numbers, as also the varia-
tions, are so dissimilar that I have adopted the followmg method
for showing the relative movements. The mean pressure through-
out the observations was 75500 mm.; the mean resistance (after
correction for temperature of coils) was 1792°546 of my box unit
(1 box unit = ‘01 ohm approximately). In columns 2 and 3 I give
the differences from these means respectively at the given times*,
the barometer differences are then plotted on 10 times the scale
of the resistance differences, and thus the paths of the two
irregular curves are brought comparatively near together. It is
evident that hardly any signs of lag are observable; in fact, if
there is any lag, it would appear to be rather in the barometer
than in the temperature of the steam. In column 4 I give the
boiling poimt reduced from the pressure according to Regnault’s
* The times were only recorded to the nearest minute, further accuracy being
unnecessary.
1896.) Mr Griffiths, On Thermometric “Fixed Points.” 229
experimental values as revised by Moritz. (The barometer read-
ings are corrected for temperature and for g to sea-level latitude
45°.)
The mercury standard barometer used has been recently com-
pared with a Tonnelot barometer in the possession of Mr Heycock
which was standardised by Dr Guillaume in the spring of this
year, and I may remark that a discrepancy of as much as ‘2mm.
would appear to exist between the Sevres and Kew standards if
the comparisons of my #-inch barometer are to be trusted. The
conditions of the comparison with Mr Heycock’s barometer, how-
ever, were not entirely satisfactory, and I hope to have an
opportunity of repeating them under more favourable circum-
stances. I cannot therefore speak with certainty as to the absolute
value of the pressure which, however, is immaterial for our present
purpose.
An error of (05mm. in a barometer reading corresponds to
0°:001 in the boiling point, and great precautions, therefore, are
necessary to ensure sufficient accuracy. If the barometer is con-
tinually handled when resetting during a series of observations,
the thermometer attached to the instrument does not truly
indicate the temperature of the mercury in the barometer tube.
The compensated sulphuric acid barometer of Professor Callendar
and the writer’s does not require handling, its scale is nearly six
times as open as the mercury scale, and its readings are inde-
pendent of temperature changes. It cannot, however, be relied on
for absolute readings, one reason being the permanent shrinking
of the glass bulb which is similar in nature to that characteristic
of mercury thermometers. The plan I have adopted, therefore, is
as follows. At regular intervals of about 20 minutes a careful
reading of both barometers is taken, the mercury barometer being
left untouched with the case shut throughout the interval, while
at intermediate times the sulphuric acid barometer is read through
a telescope and the absolute values deduced by interpellation from
the comparisons at each end of the interval.
The following arrangement ensures great accuracy in the
setting of the ivory point, which is a frequent cause of error in
mercury barometer readings. The cistern is entirely surrounded
by a covering of black paper, with the exception of a small window
in front and another behind the ivory pot. The point of view
is thus always the same. Across the further window is placed
a very thin black line whose image is seen in the mercury
across that of the ivory point. This image is viewed through a
powerful magnifying glass and the curvature of the line can be
seen before the dimple is apparent. I would strongly recommend
this method, for I find that great accuracy results from its
adoption.
230) = Mr Griffiths, On Thermometric “Fired Points.’ [Nov. 23,
The numbers in Col. v. are obtained directly from the platinum
thermometer readings whose constants are as follows:
PAW IsA34. so — lpi Op,
R, = 1293-947 dR :
R —1793°434*
e |), p: =100+ 4:9195
and as the numbers given in Col. 11. are the differences from
1792°546, by substitution we get
d — ‘888
b. p. = 100 + ——____ “49195 °
where d is the difference as given in Col. II.
The last figure of the numbers in Col. II. was read directly
from the box-vernier without any estimation of intervals—the
galvanometer showing a distinct deflection for a difference of ‘001.
dR
Since aE at 100° = 492 approximately,
it follows that a difference of 5 in the last figure corresponds to
0°-001, hence the scale even as regards pressure is nearly twice as
open as that of a barometer whose vernier reads to ‘01 mm. and
thus, provided there is no lag, a more accurate determination of
the pressure can be made by this thermometer than by observing
the barometer itself.
The barometer observations were taken by one observer at the
same instant as the other read the resistance indicated on the
box.
An inspection of this table will I think convince the most
sceptical that the temperature lag of the steam may be dis-
regarded. It appears astonishing that the temperature adjustment
should be so rapid, especially when a sudden fall such as that
shown from 2.30 to 3 p.m. supra takes place. Here the cooling
can only be caused by excess of evaporation, and when one reflects
on the mass of copper, &c., bounding the enclosure, the rapidity of
adjustment is surprising.
I should mention that the hypsometer is of a somewhat
unusual form and that special screens are used both below and
above the thermometer bulb.
* These values of the constants were obtained subsequently, and are qnite
ce of the observations on Oct, 7th.
1896.] Mr Griffiths, On Thermometric “Fired Points.” 231
Results of Boiling Point determinations, Oct. 7, 1896.
I II
III IV | Vv
Time | Bar. — 755-00 | R—1792°546 || B. P. from bar | B. P. from therm.
(corrected) readings
m.m ° fe)
1.35 + 85 99-848
1.464 + 1:03 +177 855 99°855
1.48 + 1:03 +179 B55 856
2.23 + 1:10 +183. . 857 857
2.29 oo + 167 | 854 852
2.33 + ‘81 +142 || 847 848
2.44 + 60 | 839
2.51 + 44 | +:075 833 835
2.53 + :29 + 047 828 829
2.58 — ‘20 — 042 810 ‘811
3.0 —- 39 | --073 803 805
3.2 — ‘54 — 109 ‘797 won
3.9 — ‘94 — 180 ‘782 783
3.21 — 96 — 185 Tol ‘782
3.23 — 93 — 174 ‘783 “784
3.27 — 85 — 163 ‘786 ‘786
3.29 — 80 — ‘152 ‘788 ‘789
3.30 - ‘77 —-'146 | ‘789 ‘790
3.33 = 18 S150. | ‘788 ‘788
It thus appears that our present definition is sufficient from a
practical standpoint for, since there is no lag, the same conditions
can be reproduced by different observers with sufficient accuracy
dt
dp
sufficiently accurate. From a theoretical point of view, however,
the conditions are by no means perfect. We require a standard
_ absolute pressure, the value of which can be stated without our
present arbitrary method of reference to a mercury column, and it
seems fitting that the attention of physicists should now be directed
to this question. The effects of any change, however, would be so
far-reaching that I doubt if I should have ventured to express my
own views on this matter had it not been for the powerful support
afforded by a letter I have recently received from Professor Hicks,
F.R.S., of Sheffield. He has been so kind as to give me per-
mission to make what use I please of that letter, and I cannot
close this communication better than by transcribing it almost in
full.
and, further, Regnault’s values of — are, for pressures near 760,
232 Mr Griffiths, On Thermometric “Fired Points.” [Nov. 25,
Sane It is time to come to some determination as to the value
of the normal pressure—on which indeed all thermal units of
measurement ultimately depend. At present we define standard
pressure as that of 76 cm. of mercury at 0° in Paris—a complicated
and roundabout method which depends on a local value of gravity,
a temperature, and a density......
“The natural standard of pressure—10° dynes per sq. em.—is, as
is well known, very nearly the same as the present standard of
76cm. I find that a column of mercury 75 em. (three-quarters of
a metre) high at 0° at sea-level in latitude 45° exerts a pressure
of (1—-00007) megadyne/cem.?, for most purposes identical with a
megadyne (in lat. 45° 1’ identical).
“T would propose then that the megadyne per sq. cm. be formally
adopted for the standard pressure to which to refer properties of
gases. The fact that it is ? the pressure of a metre of mercury at
O° in lat. 45° is convenient and may be rendered accurate either
by altering infinitesimally the height, the temperature, or the
latitude. Or, the term “atmosphere” might be kept for it.
“Jn this method instead of speaking of a vacuum of so many
millionths of an atmosphere we should say so many dynes per sq.
cm. The advantages are that the unit is an absolute one, that it
is nearly the same as that now in general use and that its value is
probably much nearer the time-mean of barometric height in the
majority of laboratories than 76 cm.
“Supposing that the absolute unit of pressure be adopted, the
100° on the new thermometer would be the temperature of steam
under one megadyne per sq. cm., which—using data given in
Kverett’s “Units”—works out to 99°62°C. The new degrees
would therefore be ‘9962 times the present ones.
“Taking again the number given in the B.A. Report for diminu-
tion of specific heat of water per 1° as 00036, and supposing it to
hold backward from 10° to 0° (which, however, can scarcely be the
case) the unit of heat (4°2 joules). would be measured by the heat
necessary to raise 1 gram of water from 0° to 1°. This last result,
if really true, is a curious coincidence and would be an argument
in favour of the change here proposed. It would define the heat
unit as at present, and at a temperature at which accuracy is in
general most easily attained.
“It may be objected that the alteration of the thermometric
scale puts the proposal outside the limits of what is practical. To
this I would observe that there are two classes of people to be
considered, the general public and the scientific world. To the
first it would make no difference, the thermometers used by them
would scarcely show the difference and as a rule they do actually
err by amounts much larger-than the change proposed. In
1896.] Mr Griffiths, On Thermometric “Fixed Points.” 233
accurate scientific thermometry it would only mean an alteration
in the table of corrections for each instrument, and in translating
old results it would simply mean multiplying by a factor
Pe 0038......-. %
I may say that I am in general in hearty accord with the
propositions advanced by Professor Hicks although, at the same
time, we differ on one or two minor points.
The conclusions I have arrived at may be summed up as
follows :—Our present definition of the freezing point is theoreti-
cally sound but practically impossible; our present definition of
standard boiling point is practically satisfactory while theoretically
capable of improvement.
VOL. IX. PT. IV. 18
THE COUNCIL.
(Elected Oct. 26, 1896.)
President.
F. Darwin, M.A., F.R.S., Trinity College.
Vice-Presidents.
G. D. Liveing, M.A., F.R.S., Professor of Chemistry.
A. Newton, M.A., F.R.S., Professor of Zoology.
J. J. Thomson, M.A., F.R.S., Cavendish Professor.
Treasurer.
R. T. Glazebrook, M.A., F.R.S., Trinity College.
Secretaries.
H. F. Newall, M.A., Trinity College.
W. Bateson, M.A., F.R.S., St John’s College.
H. F. Baker, M.A., St John’s College.
Ordinary Members of the Council.
. A. Ewing, M.A., F.R.S., Professor of Mechanism.
. H. Neville, M. A. , Sidney College.
. H. Griffiths, M.A., E.R.S., Sidney College.
. B. Hardy, M.A., Gans and Caius College.
Sir G. G. Stokes, Bart., Se.D., LL.D., F.R.S., Lucasian Professor.
A. Sedgwick, M.A., F.R.S., Tanity College.
A. Scott, M.A., Trinity College.
W. H. Gaskell, M.D., F.R.S., Trinity Hall.
J. E. Marr, M.A., F.R.S., St John’s College.
J. Larmor, M.A., F.R.S., St John’s College.
H. Marshall Ward, Sc.D., Professor of Botany.
A. E. Shipley, M.A., Christ’s College.
PROCEEDINGS
OF THE
Cambridge Philosophical Society.
Monday, January 25, 1897.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
The following Communications were made:
(1) Some results obtained by staining the Brain with the
Chrome-silver method (illustrated by photo-micrographs). By
Dr A. HILt.
Dr Hill showed a granule of the olfactory bulb with a looped
axis-cylinder, and also certain forms of granule of the cerebellum
not hitherto described. He also exhibited sections and photo-
graphs showing the variations in the form of the “ thorns” on the
dendrites of nerve-cells which can be produced by varying the
hardening process. (1) The thorns may be absent. (2) They
may be long or short. (3) They may have the typical form of a
minute rod with a dot at the end, or the dots may be divided and
lie on the course of the rod. (4) They may be replaced by long
filaments.
Dr Hill submitted the theory that the conducting filaments of
nerve-cells are continued from one neuron to another. He regards
the “thorns” as the cell-ends of the non-staining nerve-fibrils
which are invested with a film of cell-plasm. He supposes that
the extension of the cell-plasm along the course of the fibril is
VOL. IX. PT. V. 19
236 Mr Lnster, The young of the microspheric forms [Jan. 25,
necessary for the conduction of impulses and thinks that the
amount of this film varies, resulting in the variations in the state
of “openness” or inhibition of the reflex path.
(2) A possible explanation of the quinqueloculine arrangement
of the chambers in the young of the microspheric forms of Triloculina
and Biloculina. By J. J. Lister, M.A., St John’s College.
In the later stages of growth of the shells belonging to the
genus Biloculina the arrangement of the chambers is very simple
(Figs. 1—3). They are disposed on either side of an axis, the mouth
being directed alternately to one and the other end of this axis,
and the median plane which divides any single chamber symmetri-
cally, is also the median plane of the whole series of the chambers
added during the later stages of growth. In the megalospheric
ie. 1. Biloculina depressa d’Orb. Megalospheric form, longitudinal section.
x o.
Fig. 2. Transverse section of a specimen with a smaller megalosphere of the
same species. x 50
form (Figs. 1 and 2) this arrangement is followed from the
beginning, that is to say, the two chambers succeeding the megalo-
sphere and all subsequently formed chambers are so disposed.
1897.] of Triloculina and Biloculina. 237
In the microspheric form of this genus however, as has been
admirably shown by M. Schlumberger, the arrangement of the
chambers is at first on a different plan (Fig. 3), namely, that
Fig. 3. Transverse section of the microspheric form of the same species. x 90
(Two external chambers have been omitted from the figure.)
which characterises the genus Quinqueloculina during its whole
growth. In the shells of this genus (Fig. 4) the chambers are
Fig. 4. Transverse section of the megalospheric form of Quinqueloculina
undulata d’Orb. x 100.
Figs, 1—3 are from Schlumberger, ‘‘ Revision des Biloculines des grands fonds.”
Mém.d.l. Soc. Zoologique de France, Tome tv. année 1891, p. 155. Figs, 1, 2, and 4.
Fig. 4 from ‘Monographie des Miliolidées du Golfe de Marseille,” by the same
Author. Mém. d.l. Soc. Zoologique de France, Tome vi. année 1893, p. 57. Fig. 23.
disposed on the sides of a long axis, and the mouth is directed
alternately towards one and the other end of the axis, but the
19—2
238 Mr Lister, The young of the microspheric forms [Jan. 25,
plane dividing any single chamber symmetrically, is not identical
with the corresponding plane of the preceding chamber but
directed at a definite angle to it. It is as though in a Biloculina
shell, while the plane in which the new chambers were formed
remained constant, the long axis were rotated through a definite
angle in the interval between the formation of each chamber and
the completion of its predecessor. The result is that the walls of
several chambers take part in forming the external contour of the
shell. In Quinqueloculina five chambers take part, at any given
stage of growth in forming the contour. In Z'riloculina where the
“yotation of the axis” is through a different angle the contour
presented by the shell is formed by three chambers.
In the microspheric form of the genus Biloculina the arrange-
ment of the chambers which succeed the microsphere is at first on
the quinqueloculine plan, then on the triloculine, and it is not till
several chambers have been formed that the biloculine plan is
attained.
Similarly M. Schlumberger has shown that in the genus
Triloculina the chambers are at first arranged on the quinque-
loculine plan in the microspheric form, the triloculine plan being
attaimed later.
What is the explanation of this remarkable change in the
mode of growth in the microspheric form of Biloculina and Trilo-
culina ? And why should it be characteristic of the microspheric
form, while the megalospheric form attains the arrangement of
chambers characteristic of the genus to which it belongs from the
beginning of its growth ?
It appears possible that the explanation is to be found from
the consideration of the different ways in which the two forms are
produced.
In dealing with the life history of Polystomella I have shown
that there is good reason to regard the megalospheric and micro-
spheric forms of the Foraminifera as belonging to different
generations. The megalospheric form is produced by an asexual
process—the protoplasm of the microspheric parent emerging
from the shell and breaking up into a number of spheres, the
megalospheres, the initial chambers of the megalospheric form.
The precise origin of the microspheric form is not yet clearly
made out, but there is some evidence in support of the view that
it results from the conjugation of the zoospores produced by
the megalospheric form, that is, that it is produced by a sexual
process.
The relative sizes of the zoospore and microsphere, and the
scarcity of the microspheric form as compared with the megalo-
spheric are in favour of this view and Schaudinn’s observation of
1897. ] of Triloculina and Biloculina. 239
the conjugation of zoospores in Hyalopus*, a form however in
which dimorphism has not been shown to exist, yields it consider-
able support.
If we apply this probable, though still insecure result to the
problem presented by the Miliolide, we find that while the
asexually-produced megalospheric form has a direct development,
the sexually-produced microspheric form goes out of its way to
repeat the arrangement characteristic of allied forms before it
attains the arrangement proper to its own genus.
Is not this a particular instance of a phenomenon widely met
with in higher forms of animals, in which the individuals produced
by budding attain the adult structure by a direct development,
while those produced from the egg often develope by an indirect
course, going out of their way to repeat lost features characteristic
of the archaic forms of their race? To give an instance, the
ascidians belonging to the genus Clavellina develope asexually by
buds which grow out from the stolons at the base of a colony and
are fashioned directly into the adult form, while the result of the
development of the fertilised egg of Clavellina is to produce a
tailed larva wholly unlike the parent and recalling the free
swimming Appendicularie.
In the case of higher animals the larval stages are lost, the
body of the larva being fashioned into that of the adult, but in
this group of the Protozoa, the Miliolide, the peculiar structure of
the young is permanently recorded, being built in and retained in
the centre of the chambers subsequently added.
While many of the biloculine and triloculine forms of the
Miliolide present the contrast in the mode of growth of their
megalospheric and microspheric forms, above described, in a very
marked manner, I feel that the case in favour of the explanation
here offered is to some extent weakened by the existence of excep-
tions presented by certain species belonging to the trematophorine
Miliolide, and especially by Jdalina antiqua (d’Orb. sp.), whose
structure has been elucidated by M. M. Munier-Chalmas and
Schlumberger f. .
In this species, whose growth in its later stages is mainly on
the biloculine type, the first formed chambers of the megalospheric
form are in some cases, though not in all, disposed as in the
microspheric form, on the quinqueloculine plan. Here then both
megalospheric and microspheric forms of the species may, in the
early stages of growth go out of their way to repeat the mode of
growth characteristic of the genus Quinqueloculina. The authors
point out that the megalospheric form does in some cases grow on
* Sitz. Ber. Gesellsch. Naturforsch. Freunde Berlin, Jahre. 1894. :
+ Note sur les Miliolidées trématophorées. Bull. de la Soc. Géologique de
France. 3° Ser. t. xm1. (1885), p. 273.
240 Mr Larmor, On the theory of Osmotic Pressure. [Jan. 25,
the biloculine plan throughout, and when it does not, the bilocu-
line arrangement is sooner reached, that is after the formation of
a smaller number of chambers, than in the case of the micro-
spheric form. The exception does however appear to detract in
some measure from the sharpness of the contrast in the mode of
growth of the two forms, and, though I think without altogether
annulling it, from the force of the explanation which I have
offered.
(3) On the theory of Osmotic Pressure. By J. LAnmor, M.A.,
F.R.S., St John’s College.
As osmotic theory is now attracting general attention in this
country, it seems desirable that all the positions that are maintained
in regard to it should be clearly set forth. The excuse for offering
the following remarks is that for some time I have paid attention
to the subject in its relation to general molecular theory, both in
the thermal and the electrical aspects. I fail to recognize how the
validity of the thermodynamic basis of the law of osmotic pressure
can be shaken : and though the idea of ionic dissociation in solutions
is an additional hypothesis which must be judged separately by
the extent of its agreement with the facts, it appears to me that
in some form—possibly not at all in the chemical imagery with
which it is at present often expounded—it holds the field. It is
difficult in fact to see how the hypothesis that the same chemical
element can have different valencies in different series of compounds,
which is now usually accepted, is fundamentally any whit less
paradoxical than the hypothesis of ionic dissociation; anything
that throws light on the real nature of the one must also illuminate
the other.
In his recent note on this subject*, Lord Kelvin appears to
allow, within certain limits, the cogency of the argument which
bases the law of osmotic pressure on Henry’s empirical law of
solubility for gases, an argument which has recently been carefully
restated by Lord Rayleigh, having previously been employed, as
he remarks, in forms more or less explicit, by van’t Hoff, Nernst
and other investigators. The connexion thus established however
hardly amounts to a physical demonstration, because it only
deduces one empirical relation from another. Yet it seems desirable
to draw attention to the fact, which I have not seen anywhere
remarked, that this method had been employed by von Helmholtz
in 1883, two years before van’t Hoff announced his theory of the
correlation between osmotic and gaseous pressures; and that the
principles given by him on an investigation of the work-equivalent
of gaseous solution, made in connexion with the theory of galvanic
* Proc. R. 8. Hdin., Jan. 1897; Nature, Jan. 21, 1897, p: 272.
1897.] Mr Larmor, On the theory of Osmotic Pressure. 241
polarization *, involve in fact an implicit prediction of the osmotic
law. This circumstance, that the law of osmotic pressure, as
regards dissolved gases, is tacitly involved in von Helmholtz’s
equations, does not of course confer on him a position in the actual
development of the subject.
But the theory of osmotic pressure can I think be placed on a
purely abstract basis independently of the law of solubility of gases,
which would then assume the form of a deduction from it. The
broad principles on which this is to be done have been in fact
laid down in a precise and very general manner, but without special
application, by Willard Gibbs as early as 1875, in his fundamental
development of the laws of mechanical availability of energyf.
The following position is, I believe, sound. Each molecule of the
dissolved substance forms for itself a nidus in the solvent, that is,
it sensibly influences the molecules around it up to a certain
minute distance so as to form a loosely connected complex, in the
sense not of chemical union but of physical influence. The laws of
this mutual molecular influence are unknown, possibly unknowable ;
but provided the solution is so dilute that each such complex is,
for very much the greater part of the time, out of range of the
influence of the other complexes, as for instance are the separate
molecules of a free gas, then the principles of thermodynamics —
necessitate the osmotic laws. It does not matter whether the
nucleus of the complex is a single molecule, or a group of molecules,
or the entity that is called an ion: the pressure phenomena are
determined merely by the number of complexes per unit volume.
To determine the osmotic forces, we must know the change in
available energy that is involved in dilution of the solution by
further transpiration of the pure solvent into it. In finding that
change, the laws of mutual action between molecules of the dissolved
substance are not required : for there is actually no action between
them, and as soon as the solution becomes so concentrated that
such mutual action between the complexes comes in, the theory is
no longer exact. Nor are the laws of mutual action between the
molecules of the dissolved substance and those of the solvent
required, because the effect of transpiration of more of the solvent
into the solution is not in any way to alter the individual com-
plexes. The change in available energy of the system, on dilution,
thus solely arises from the expansion of the complexes into a larger
volume; and it can be traced into exact correlation with the change
* H. von Helmholtz, “Zur Thermodynamik chemischer Vorgiinge 111”; in
collected papers Vol. 111. pp. 105—114, especially his equation (4), and the theory of
diffusion at the end. [The law had also been formulated explicitly in this manner
by Willard Gibbs as early as 1876, loc. cit. infra, p. 227.] ;
+ Trans. Connecticut Academy, Nov. 1875, p. 138, ‘ Effect of a Diaphragm
(Equilibrium of Osmotic forces).”’
242 Mr Larmor, On the theory of Osmotic Pressure. [Jan. 25,
of available energy that occurs in the expansion of a gas. This
argument meets the objection that a true theory should involve a
knowledge of the molecular actions between the various molecules.
It would seem that with just the same cogency it might be argued
that a real investigation of the connexion of the alteration of the
freezing point of a liquid by pressure and its change of volume on
freezing should involve a knowledge of the individual molecular
actions in the liquid: and so it would, had we not the means of
evading considerations of molecular constitution that is afforded by
Lord Kelvin’s great principle of dissipation, which is for this very
reason at the basis of all physical theory.
There is however one point to be remembered, namely, that the
theoretical osmotic pressure is a limiting value which may not be
reached by an actual arrangement, unless we can be certain that it
works reversibly and so without heating effects.
The remark has been made by Lord Kelvin, that the connexion
between Henry’s law and the osmotic law must break down when
the solution of the gas is accompanied by change in its state of
molecular aggregation. It is also probable from the fundamental
ideas as to dissociation and aggregation, that such change would
usually be partial, and not uniform over all the dissolved molecules ;
so that it is not to be expected that Henry’s law would in such
circumstances hold good. The point in which the argument, as
set forth in precise form by Lord Rayleigh*, becomes then inap-
plicable, is that the gas expelled from solution by the osmotic
process must be considered as emerging in the actual state of
aggregation differing from that of its free condition, and its return
to the latter state involves further change of available energy.
If the considerations above stated, which will be most suitably
developed in detail in another connexion, are valid, it follows. that
Professor Poynting’st recent suggestion with a view to evading the
necessity of the ionic dissociation hypothesis cannot avail, as it
would not lead to the desired value for the osmotic pressure: that
pressure depends on the number of molecular complexes involving
the dissolved substance that exist on the dilute solution, but not
on their dividual degrees of complexity.
* Nature, loc. cit., p. 254. + Phil. Mag. Oct. 1896.
1897. ] Prof. Thomson, On the Cathode Rays. 243
Monday, February 8, 1897.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
Dr A. C. Happon, Christ’s College, was elected a Fellow of the
Society.
The following Communications were made :
(1) On the Cathode Rays. By Professor J. J. THOMSON.
The experiments described in this paper are of two kinds: the
first set are on the electric charges carried along the rays, the
second on the deflection produced in these rays when they traverse
a uniform magnetic field.
In the experiments on the electrical effects produced by the
rays, the cathode, a plane disc, was placed in a small side tube
fused on to a large bulb; between this tube and the bulb there
was a thick earth-connected metal dise with a slit in it; a pencil of
cathode rays shot through this slit into the bulb. In the bulb on
the side opposite to the slit there was an arrangement similar to
that used by Perrin in his experiments on the charges carried by
the cathode rays; it consisted of two cylinders, one inside the
other; the outer cylinder was connected with the earth and the
inner cylinder (which was insulated from the outer) was connected
with one pair of quadrants of an electrometer. Slits were cut in
the cylinder so that the cathode rays could pass through the shits
into the inside of the inner cylinder. The cylinders were placed
at a considerable distance from the direct line of the rays, so that
unless the rays were deflected by a magnet they did not enter the
cylinder. The charge in the cylinder produced by each make and
break of the coil was investigated. A slight charge was found
to pass into the cylinder even when it was not in the direct line
of the rays, due probably to a diffused charge sent out from the
tube through the slit into the bulb at each discharge of the coil ;
this charge was small; it was generally negative but at high
exhaustions was frequently positive. When the rays were
deflected by a magnet so as to pass inside the cylinder the
cylinder received a strong negative charge; the charge was large
as long as the phosphorescent patch was stopped by the cylinder,
small when by the motion of the magnet the patch was removed
to one side or another of the cylinder. This experiment seems
conclusively to show that there is a flow of negative electricity
244 Prof. Thomson, On the Cathode Rays. [Feb. 8,
along the cathode rays. The following experiments show however
that there must be something besides a stream of negatively
electrified particles along the cathode rays. If the coil is kept
running the negative charge in the cylinder does not increase
indefinitely, it reaches a certain limit and then remains constant,
though the cathode rays keep pouring into the cylinder, and
further if the inner cylinder be charged negatively to begin with,
then if this charge exceeds a certain amount, though the insulation
is perfect when the rays are not playing upon the cylinder, yet as
soon as the rays fall upon it some of the negative charge escapes.
In the experiments on the magnetic deflection of the rays, the
rays were produced in a side tube and sent into a large bell jar
through a slit in a metallic plate. The bell jar was placed between
two coils arranged as in a Helmholtz galvanometer so as to pro-
duce a uniform magnetic field. The rays in their course through
the bell passed in front of a glass plate ruled into squares.
A large number of photographs of the rays were taken in different
gases and at various degrees of exhaustion. The following were
some of the results obtained.
The magnetic deflection of the cathode rays in air, hydrogen,
carbonic acid gas and methyl iodide is the same provided the
mean potential difference between the cathode and the anode is
the same.
Coming through the slit there are certain ‘rays’ which are
not deflected by a magnet: these have little if any power of pro-
ducing phosphorescence. ‘The path of the rays for the first part
of their course was very approximately circular.
(2) On Electricity in Gases and the formation of Clouds in
Charged Gases. By J.S. Townsenp (M.A. Dub.).
1. Of all the electrical phenomena with which we are
acquainted there are few more interesting from a scientific point
of view than those which are to be found in gases. The branch of
the subject which is treated of in this paper is that which is
related to the properties of gases having an electrostatic charge.
No attempt is made here to give an account of the different
methods that have been employed to charge gases, as 1b is my
intention merely to enumerate some of the more important results
arrived at while investigating this subject.
2. Even with their rough methods of detecting electrification
Laplace and Lavoisier knew that the hydrogen evolved when a
metal dissolves in an acid carries with it a charge. It is therefore
all the more remarkable that with the present delicate methods of
detecting electric charges the question of electrification by natural
processes, in contradistinction to artificial methods should have
1897.] Mr Townsend, On Electricity in Gases ete. 245
attracted so little attention. The greater part of this paper is
devoted to an account of the electrification of gases which are
given off when a liquid is decomposed by an electric current,
being the most noteworthy result which I have arrived at while
examining the charges on newly prepared gases. Under certain
circumstances gases can be obtained by this method which have
an electrification, ten or twenty times greater than that which can
be given them by artificial processes. I find also that these gases
possess the remarkable property of forming a dense cloud when
they come into contact with moisture. The density of the cloud
increases with the density of the charge, and so distinctly does
this property manifest itself that a dry gas, charged even with a
density of electrification one-twentieth of that which can be
obtained, forms a distinctly visible cloud when it comes into the
moist atmosphere of the room.
3. It is necessary here to describe some principles which will
be frequently used in the course of the followmg experiments.
In order to distinguish between cases when a gas, or the dust or
spray it may contain, carries the charge it is sufficient to send the
gas through a series of fine gauzes or through a tube containing
glass wool; by so doing not more than 20 or 30 per cent. of the
charge will be lost if the gas is electrified, but if the electricity
resides on the dust or the spray it will be completely removed by
filtering through the wool. In the case of a gas, the discharging
power, or the fraction of the charge left behind on any apparatus,
varies greatly according to the rate at which it is sent through,
being less for the greater velocities. There is another very
striking difference between the behaviour of a charged gas and
that of a collection of small charged particles when left in a vessel,
namely: the gas retains its charge for a considerable time, while
a collection of small charged particles rapidly discharges against
the sides of the vessel. This difference will also serve to dis-
tinguish between the two cases.
4. Let J, fig. 1, be an insulated inductor, the outer surface
being made a conductor by covering it with tinfoil, and when it is
connected to the insulated quadrants of the electrometer the
motion of the spot of light (reflected from the mirror attached to
the needle), on the scale will register the quantity of electricity
entering or leaving J. If the air from the room be blown into J
from a blow-pipe bellows through a plug of glass wool the position
of the spot of light will not be affected, but if the tube containing
the wool be removed and the air be blown directly in from the
indiarubber tubing it will be found that the electrometer shows a
large positive charge on J. This charge was unable to pass
24.6 Mr Townsend, On Electricity in Gases [Feb. 8,
through the tube containing the glass wool, and if this be now
replaced on the end of the indiarubber tubing it will be found
impossible by blowing unelectrified air into J to displace any
of the charge that had been put in after it had been there for the
space of half a minute.
We have a simple explanation of this result by supposing the
charge to be distributed over a small number of carriers, each
having a relatively large charge, but in the case of a gas with an
equal electrification per c.c. the number of carriers is very much
larger and the charge on each proportionally smaller, being
probably the atomic charge, so that the force due to their mutual
repulsion which acts on each carrier would be small, and con-
sequently a long time would elapse before they would reach the
sides of the vessel. This property of a charged gas can be
illustrated by the following experiment.
5. The electrification of hydrogen which is given off when a
metal is dissolving in an acid can be seen by pouring a 50 per cent.
solution of sulphuric acid, at a temperature of about 80°, over the
iron wire contained in the vessel A, fig. 1. The hydrogen as it is
given off is made to bubble through permanganate of potash in B,
1 ,
eee oe ee ame eee Bese)
Fig. 1.
(The dotted lines represent insulators.)
and through sulphuric acid in C, and then to pass through a
tube of glass wool W before entering 7, which is connected to the
1897.] and the formation of Clouds in Charged Gases. 247
insulated quadrants of the electrometer, the generating apparatus
G being connected to earth. These connections can be easily
made by means of the mercury cups in the paraffin block P. The
spot of light on the electrometer scale shows a large deflection
in the positive direction as the hydrogen enters J. If @ be
now removed and the hydrogen left in J for the space of five or
ten minutes it will be found that if it be then displaced by
blowing in unelectrified air that the spot of light will return
almost to the place from which it started showing that the gas
retained more than 95 per cent. of its original charge. Other
experiments similar to this showed that when a gas is left in an
inductor for the space of two hours that it still retains from 1th
to ith of its original charge.
6. With regard to the fact that the hydrogen, given off
when iron is dissolving in sulphuric acid, carries with it a positive
charge, I find that this result had previously been obtamed by
Enright, who examined the electrical properties of several newly
prepared gases, and although his investigations were incomplete,
and his results capable of different interpretations, nevertheless
they have not been accorded the credit they deserve. ' None of his
experiments were directed to finding out whether the charge was
on the gas or on the spray, but he unhesitatingly assumed that
the electricity was in all cases carried by the gas. Under these
circumstances it is easy to see that some of his conclusions may
have been erroneous. (Enright: ‘Electromotive force of contact
between a liquid and a gas, Phil. Mag. 1890; Nature, vol. 36.)
Enright’s experiments were repeated by Brown (Brown:
‘Electrification of the Effluvia from Chemical or from Voltaic
Reactions’), who found that all the experimental results were
quite correct. No new light was thrown on the matter; the
conclusion which the experimenter himself arrived at was that it
was impossible to decide whether the gas or “ effluvium,” which it
carries with it from the acid in which a metal is dissolving, is
charged, the balance of evidence being in favour of the latter.
Professor Lodge (Phil. Mag. 1890; Nature, vol. 36) attributed the
cause of the electrification which Enright observed to the well-
known electrification of spray, but the following experiment will
show that his interpretation was wrong.
7. The experiment which Enright performed and from which
he drew his conclusions with regard to a metal dissolving in an
acid is very easily performed by insulating the apparatus G, fig. 1,
and connecting it to the quadrants of the electrometer. If the
vessel A be left open so that the hydrogen may escape directly
into the air it will be found that when a 50 per cent. solution of
248 Mr Townsend, On Electricity in Gases [Feb. 8,
sulphuric acid at about 80° is poured over two or three grammes
of iron wire that the electrometer first shows that a large positive
charge is escaping from A, and, as the process of dissolving goes
on for a few minutes, that the escape of positive electricity gets
less and less till finally a neutral stage is reached, and immediately
after this negative electricity in large quantities begins to escape
and continues to do so till all the iron is dissolved. From this
Enright concluded that at one time positive and at another time
negative electricity was carried by the gas. Further examination
however does not justify this conclusion, for if mstead of letting
the gas escape into the air from A it be made to pass through the
liquids in B and C and escape by the tube 7’ into the air it will be
now found that G loses positive electricity as before, reduced in
quantity, whereas none of the negative which in Enright’s experi-
ment is the larger of the two charges will now escape with the
gas. We see therefore that there is no evidence here that the
hydrogen carries the negative electricity, and that it is more
probable that this charge was carried by the spray which it
acquired by an inductive effect.
8. The gases which are given off by electrolysis have always
been assumed to be completely cleared of electricity. It does not
require a very delicate electrometer to show that this is not the
case; for if they are examined by any of the ordinary methods it
will be found that under certain circumstances these gases carry a
large charge which remains on the gas after it has been passed
through wool or bubbled through a liquid, and owing to the regu-
larity with which they can be produced, by keeping the current
through the electrolyte constant, the method affords an extremely
simple means of studying the properties of charged gases.
9. As far as experiments which I have already made on this
subject show, it is possible to obtain gases with any electric density
up to 5 x 10° electrostatic units. This has been found to be the
case with regard to positively charged oxygen and hydrogen which
are given off when dilute sulphuric acid is electrolysed, and also
with regard to the negative oxygen which is given off from a
caustic potash cell. The hydrogen from the latter also has a
negative charge, but it is small compared with that which is on the
oxygen, whereas in the case of the sulphuric acid cell the hydrogen
as a rule has the larger charge. The effects are in all cases
increased by raising the temperature of the cell. The charge and
sometimes even the sign is altered by impurities, but it is not
proposed here to enter into details concerning the electrolytes.
Suffice it to say that the positive gases are got from sulphuric
acid, and the negative from a caustic potash solution when a
1897.] and the formation of Clouds in Charged Gases. 249
current of about 12 or 14 ampéres is sent through them. They
have also been found to be electrified when so small a current as
two amperes is sent through them, but the rate of evolution is so
small that the larger currents have been generally used.
10. When these charged gases are bubbled through water, they
become clouded. The cloud which is thus formed can be com-
pletely removed by bubbling the gases through sulphuric acid or
sending them through a U tube of CaCl,, but when they get
into the atmosphere of the room they condense the moisture and
form a stable cloud in an unsaturated atmosphere. The process of
forming the cloud in positive or negative oxygen by bubbling
through water, and removing it again by bubbling through sul-
phuric acid, can be gone through without losmg more than 20 or
25 per cent. of the original charge on the gas. Clouds having
similar properties are formed by the hydrogen coming off a
rapidly dissolving metal.
11. Fig. 2 represents a convenient form of apparatus for
examining the electrical properties of these gases. The electrolyte
is contained in the beaker F’, and the gas which is given off from
Fig. 2.
(The dotted lines indicate insulators. )
the platinum electrode # rises into the cup C and is brought by
glass tubing to the paraffin tunnel P inside a large screen S,
which contains all the apparatus which it is desirable to connect
to the electrometer in order to measure charges. Between the
two tunnels P and Q can be put any apparatus D whose discharging
250 Mr Townsend, On Electricity in Gases [Feb. 8,
power it is required to find. The gases after passing through
D are led into an inductor by means of the tube 7’, the inductor
I being used for oxygen and J’ for hydrogen. By connecting J to
the electrometer while a fixed current is going through the cell
the quantity of electricity Q,; which the gas carries with it through
D per minute can be found, and then, with the same current
through the cell, D can be connected to the quadrants and the
quantity of electricity Q, which the gas leaves behind per minute
can be obtained. When D consists of a sulphuric acid bottle H
and a tube of glass wool W, it is found, when the gases from the
sulphuric acid and caustic potash cells are examined, that they
have a large charge when they enter an inductor. This charge
depends very little on the liquid which is in H, but is considerably
reduced by packing the wool very tight in W. The discharging
2
Qi + Q
through the apparatus; this can be seen by increasing the current
through the cell. But as this is almost a self-evident fact we will
pass on from it and describe a series of more important experi-
ments. .
power varies according to the rate at which the gas is sent
12. In the following experiments the discharger D between
P and Q consisted of a bottle H into which various liquids could
be placed and also a tube of glass wool W’. Instead of leading
the gas from the cell directly into P, it was passed first through a
bottle H’ outside the screen so that on putting sulphuric acid into |
H’ the gas was led into D perfectly dry, and by substituting
water for the sulphuric acid in H’ the gas entered P carrying
with it a cloud. The liquid whose effect upon the charge on the
gas is to be tested is placed in H, and sulphuric acid in H’, and
after the current has been running for a sufficiently long time to
drive out the uncharged air from the apparatus, D is connected to
the quadrants and the number of divisions NV, which the spot of
light on the electrometer scale passes over per minute is observed.
The inductor J is then connected to the quadrants and D put to
earth, and the number of divisions V, that the spot passes over
per minute, due to the charged gas entering J, is then found.
It is necessary to blow all electrified gas out of J before begin-
ning to find N,, as this number would be diminished if any
electrified gas were to be escaping from J while the observations
were being made. The sulphuric acid is then removed from H’
and water put in its stead, and two similar numbers iV,’ and WV, are
then obtained, the same current flowing through the cell as when
NV, and NV, were being determined.
The following table contains the numbers thus obtained for
sulphuric acid, water, and potassium iodide solution, in H.
1897.] and the formation of Clouds in Charged Gases. 251
These numbers give accurately the effect, on the discharging
power due to the presence of a cloud, as no change was made in D
M N, Ny My
Sulphuric acid in # ...... 27°5 18 30 17
\ CU Rs er 26 22 28°5 18
KI solution in 7 ......... 27 17 32 15
Gas entering the liquid/|Gas entering the liquid
dry carrying with it a cloud
while water was being substituted for sulphuric acid in H’. In
order that the relative discharging powers of sulphuric acid, water
and KI solution should be obtained to the same accuracy, the
depth to which the tube in H dips into the liquid should be very
accurately adjusted. But seemg that in these experiments a
large part of the discharging power is due to the glass wool no
particular precautions were taken to ensure this, but the tube
was dipped under the liquids in each case to equal depths as
accurately as the eye could judge.
13. The above numbers were obtained from experiments with
negative oxygen, and as far as they and several similar experiments
show, there is no increase, but rather a diminution in the dis-
charging power of D, both in the case of positive and negative
oxygen, when potassium iodide solution is substituted for sul-
phuric acid or water in H. So that the question of the ozone
being the carrier of electricity is inadmissible, as is also the
suggestion that the cloud consists of hydrogen peroxide, for not
only is the charge not removed by being sent through the
potassium iodide solution, but when the dry gas is led into this
solution the cloud appears in the space in H above the solution.
14. When we consider the first series of numbers, which show
that the removal of the cloud by sulphuric acid does not discharge
the gas even to the same extent as bubbling the dry gas through
the same acid, it might at first sight appear that the cloud and
the charge had nothing to do with one another. It must however
be remembered that only a very few of the drops forming the
cloud come into contact with the acid, and the disappearance of
the greater number of the drops is due to evaporation caused by
the lowering of the vapour pressure by the sulphuric acid, and we
have thus a good example of vapour coming off a charged sphere
without carrying with it any of the charge. (See J. J. Thomson,
Recent Researches in Electricity and Magnetism, page 54.)
15. This evidence showing that the carriers of the electricity
VOL, 1X. PT. v. 20
252 Mr Townsend, On Electricity in Gases [Feb. 8,
must be the gas is supported by a series of experiments of quite
a different kind which were done with the negative oxygen from
the caustic potash cell. A small mductor containing some
sulphuric acid in the bottom was insulated and connected to the
quadrants, and the charged oxygen then admitted, the spot of
light having gone n, divisions negative. ‘The inductor was then
corked and the acid shaken up with the gas for 1} minutes and
then again insulated and connected to the quadrants, when on
removing the cork and blowing out the oxygen it was found that
the spot of light went in the positive direction, giving say n,
divisions. This showed that the gas retained n,/n, of its original
charge. The actual values obtained in two experiments of this
sort were n, = 56, n,= 36 and n,=66, n,=39. This experiment
was repeated with strong pyrogallic acid instead of sulphuric acid
and it was found that a considerable fraction, about 45 per cent.,
of the charge remained on the gas, and could be blown out. The
pyrogallic acid was left in the inductor and some strong caustic
potash added, and a fresh quantity of charged oxygen was then
put in and shaken up with the potassium pyrogallate for exactly
the same time, 14 minutes, as in the case of pyrogallic acid, and it
was now found that only about 8 per cent. of the charge could be
blown out, showing that, of the 45 per cent. which would have
remained if no absorption of oxygen had taken place, more than
eight parts in ten have now been removed from the air in the
inductor. The numbers which were obtained in three experiments
of this kind are given in the followmg table; n, the charge (in
divisions of the scale) put into 7 when it contained pyrogallic acid,
and n, the charge which was blown out after shaking up with the
acid for 14 minutes, n, the charge put in after KOH had been
added, and n,’ the charge blown out after shaking up with the
pyrogallate for 14 minutes.
85 39 65 4
16. If the electrification resides on the drops when the cloud
is formed, it ought to be possible to diselectrify the gas by forming
a cloud in it and then letting the cloud fall in a vessel. This is in
fact what does occur, for if the gas be thoroughly dried by passing
it through two sulphuric acid bottles and then let into an
inductor with sulphuric acid in the bottom only a very slight
1897.] and the formation of Clouds in Charged Gases. 253
cloud is formed, and after leaving the gas in the inductor for
five minutes almost the whole charge is carried out when un-
electrified air is blown in; but if instead of having sulphuric acid
in the bottom of the inductor some water be put into it, so that
when the gas is admitted a dense cloud forms, it will now be
found that after the lapse of five minutes only about half of the
original charge can be blown out—the remainder having been
carried to the surface of the water by the falling of the cloud.
The Tables I. and II. contain the numbers, which were
obtained in experiments of this kind, NV, denoting the charge
put into the inductor (in divisions of the scale) and NV, the charge
blown out after five minutes. Table I. refers to the case where
sulphuric acid is in the bottom of the inductor, and Table IT. to
the case where water was in the bottom of the inductor and a
cloud formed, 7’ the number of minutes taken to put in the gas.
TONE «he Pl ie ule
4 344 | 33 4 42 | 21
TABLE I. TABLE II.
1/70 ©} /60 14 | 87 | 40
3 36 | 34 3 315] 165
17. In order to weigh the cloud and at the same time find
the electrification two methods were adopted. In the first method
Fig. 3.
(The dotted lines indicate insulators.)
254 Mr Townsend, On Electricity in Gases [Feb. 8,
the gas was bubbled through KI solution in the bottle A, and
then dried by the sulphuric acid in B (Fig. 3), and led into the
paraffin block P. Between P and Q there are two small test-tubes
fitted up as shown, the first X containing water and the second Y
sulphuric acid; they were covered with tinfoil # and a ther-
mometer J’ gave the temperature of the tubes. When the
thermometer came to a fixed temperature the bath C in which
A and B were immersed was adjusted to the same temperature.
The gas as it entered P being dry removed from X not only a
quantity of vapour to saturate the gas, but also a dense cloud,
both the vapour and cloud being removed by the sulphuric acid
in Y, so that the gas escaped from Q in the same state as it
entered X. The tubes X and Y were weighed before being put
into position, and when the temperatures of A and B were made
the same as 7 a stream of electrified gas was passed through the
apparatus for about 10 minutes, during which time the mductor
I and the discharger D were alternately connected with the
electrometer for periods of two minutes to find the rate at which
each was gaining a charge. The tubes X and Y being weighed a
second time it was generally found that XY lost more weight than
Y gained, so that it was found necessary to put wool in the upper
parts of the tubes, that in X being soaked with water, and that in
Y with sulphuric acid. The results of these experiments were
not quite satisfactory on account of the difference of weight,
which occurred chiefly when the stream of gas was irregular, as it
sometimes rushed too fast for the sulphuric acid to remove its
moisture. On this account the method is only suitable for
oxygen, when about 12 or 14 amperes are running through the
cell. The results obtained for the negative oxygen were con-
sistent, and the numbers shown in the table of observations show
that in the process of forming the cloud in XY and removing it in
Y only 21 per cent. of the electrification is lost when the gas is
going through at the rate of 85 c.c. per sec.
In the following table, which gives the result of these experi-
ments, @ is the temperature of the water that the cloud is formed
in, 7’ the time in minutes that the stream of gas is allowed to run
through X and Y, C the current in ampéres through the cell,
N, and JN, the total charges in divisions of the scale acquired by
I and D during the time 7, W, the loss of weight of X, and W,
the gain of weight of Y in grammes.
6 T C N, WV, W, W,
10°8 12 14 332 84 0174 ‘0174
115 10 145 305 80 0161 ‘0155
1897.] and the formation of Clouds in Charged Gases. 255
When J was connected with the electrometer one division of
the scale denoted -00405 electrostatic units of electricity, and
when D was connected each division denoted ‘00429 absolute
units.
From these observations we get the electrification per c.c. and
the corresponding weight of cloud—it being assumed that the
electricity passing from X to Y is Q,+ : ,
Q, being the quantity of electricity that enters J,
Q, being the quantity of electricity left on D.
18. Positively electrified oxygen and hydrogen were also sent
through this apparatus in order to be able to compare the dis-
charging powers, and it was found that for positive oxygen given
off by 14 amperes that the discharging power is ‘21, exactly the
same as in the case of negative oxygen when going at the same
rate, 85 c.c. per second. But in the case of the hydrogen the
discharging power was greater although it was going faster; thus
when there were 11°8 amperes going through the cell, the gas
going at the rate of 1°44 ¢.c. through the apparatus, the discharg-
ing power was 33 and with 13 amperes the discharging power
was ‘29.
19. The second method that was adopted to find the weight
of the cloud was arranged with a view to ensure the complete
saturation of the gas, and the complete removal of the moisture
by bubbling through a set of three bulbs containing sulphuric acid,
and then weighing the latter. The sulphuric acid bulbs were
placed between P and Q and their discharging power found by
the methods already described while a current equal to that
which it is desirable to use to form the cloud is going through
the electrolyte,—the sulphuric acid having been removed from B
(fig. 3), and water substituted in its stead. In finding the dis-
charging power it is necessary to have the paraffin tunnel P
perfectly dry inside so as to ensure insulation, and this can be
relied upon for about 15 minutes while the moist gas is being
carried through P, but it was found that a considerable quantity
of moisture was left in P, and in the small tubes which were
embedded in the paraffin, so that an error would be introduced in
the weighing. If however the discharging power be first found P
can be removed and the sulphuric acid bulbs can be connected to
the tube leading from B which has a bulb blown on it so as to
prevent any spray being carried along it. The current should be
allowed to run for about three or four minutes before putting
on the bulbs to ensure that this delivery tube from B gets
thoroughly moistened. Having found the discharging power of
the bulbs it is now only necessary to observe the charge acquired
256 Mr Townsend, On Electricity in Gases [Feb. 8,
per minute by the inductor into which the gas enters after
leaving the acid, and the total charge crossing from B to the
sulphuric acid can be calculated.
20. This method gave very consistent results, and in the case
of oxygen agreed fairly well with those obtained by the first
method. The following is a list of the observations made: C the
current through the cell in amperes, @ the temperature of the
bath in which the bottles A and B were immersed, 7’ the time
the current was on, 6 the discharging power, and W the increase
of weight of the sulphuric acid bulbs, V the number which gives
the charge in electrostatic units per degree of the scale, Z the
charge per minute on the inductor in divisions of the scale.
Positive Oxygen 14 Sie alo) 22 0185 | 00402 | -45
Pewee Deel se reer Dee Cee Heer eelseecesoee|sarenerasd Oe eeseeesseesslseseOesne
Positive Hydrogen | 12°5 | 11 15 23°5 | -0285 | 00480 | 54
see meer er leceevaseaiccesecoeelsererssceelsssereersoas oereeeraseoe|sese Hae ee
Negative Oxygen 14 11:8 | 20 20°8 | °0330 | 00402 | 46
When the weight of the moisture, carried across due to the gas
being saturated, is subtracted from the increase of weight of the
sulphuric acid bulbs we get the following numbers, which give
the connection between the charge per c.c. and the weight of the
cloud per c.c.
Positive oxygen.
Charge per c.c. in Weight per c.c.
electrostatic units in grammes
3°13 x 10-3 15 x10~6
4:06 x 10-3 20°4 x 107
Negative oxygen.
2-42 x 10-3 18-4 x 10-6 Nias as:
2°62 x 10-3 19:4 10-08 ys) euacr
30 x1l0-3 21°5 x 1076
Positive hydrogen.
| BG. SOUO- © 10°8 x 10-6
24 x1073 99x 10-6
1897.| and the formation of Clouds in Charged Gases. 257
These tables show that the negative oxygen has a denser
cloud for equal electrification than the positive gases. It is also
manifest that the weight of the cloud in each case is proportional
to the electrification, so that there can now be no doubt that the
formation of the drops is an electrical phenomenon.
21. Rough approximations can be made to the size of the
drops in the case of the electrified oxygen as the outline of the
cloud is sometimes very definite and the rate at which the cloud
falls can be found. It is convenient for this purpose to photograph
the same cloud twice, allowing three or four minutes to elapse
between the two exposures. By this means it is found that the
cloud in the positive oxygen falls at the rate of 10 mms. in three
minutes, and that in the negative at the rate of 14 mms. in three
minutes. From these observations we get the radius a of the
drop from the equation Fagan (Lamb, Motion of Fluids, p.
be
229). Taking ~ ='000185 we get for the radius of the drop in
the negative oxygen 8-1 x 10-*, and in the positive 68 x 10~.
Dividing the weight of the drop into the weight of the cloud
per c.c. the number of the drops is obtained, and dividing this
number into the charge per c.c. the charge on each is got. Thus
for positive oxygen the charge on each carrier is 2°8 x 107, and
for the negative 31 x 107”.
22. The weight of the drops forming the cloud as found by
the photographic method is not accurate to more than 8 per cent.
The tables giving the “relative ” values of the weight of the cloud
per c.c. to the electrification per c.c. are accurate to 4 per cent.,
although a slight general discrepancy exists in the charges, as the
condenser, two concentric cylinders, which was used to standardise
the electrometer had no guard ring. Hence the numbers given
above as the charges on each carrier are not more unequal than
the errors of the experiments would account for, so that there is
nothing in this result to disprove that the oxygen carriers have
the actual atomic charges. The drops in the hydrogen cloud are
more numerous than those in the oxygen clouds for the same
electrification, but I must reserve for some future occasion the
exact estimation of the charge on the hydrogen carrier, as at
present it has not been found to the degree of accuracy that is
desirable.
23. The clouds which are formed by electrified gases are
perfectly stable even in an unsaturated atmosphere, and in this
respect bear a close resemblance to atmospheric clouds. There
are other points in favour of the supposition that the condensation
of the atmospheric clouds is due to electrical causes: for instance,
it Las been amply shown in the foregoing experiments that
258 Mr Townsend, On Electricity in Gases etc. — [Feb. 8,
negatively electrified oxygen forms round it a cloud of larger
drops than the positive for the same density of electrification.
The negative cloud does on this account fall more rapidly
than the positive, so that eventually the upper layers of the
atmosphere would have a light positive charge. This is exactly
what does exist in the atmosphere, namely, that its normal state is
positive, as Lord Kelvin points out in a pamphlet on “ Electrifica-
tion of Air.” (Philosophical Society of Glasgow, 1894-5.) He
also refers to experiments of Elster and Geitel’s, which show that
when rain or snow falls into a basin it generally shows a large
electrical effect whether positive or negative, even in the space of
a quarter of a minute, with however on the whole a preponderance
of negative electrification. When we come to seek a theoretical
explanation of the formation of these clouds the way is perfectly
clear up to a certain point. It can be shown (J. J. Thomson,
Applications of Dynanucs to Physics and Chemistry, Chap. XI.)
that if a drop having an electrification # and radius a be in a
saturated atmosphere near a flat surface, then when w= a
being the surface tension of water, a particular size of drop is
obtained such that if ais less than this value, moisture will be
condensed on the drop, and when a is greater than this value, the
drop will evaporate and become smaller. So that on these con-
siderations only we get a stable nucleus HOH which in the case
of the oxygen would have a radius of =~. It would be prema-
1Ops
BG
ture to go more deeply into this subject in this paper, as experi-
ments are in the process of being carried out which may throw
more light upon it. In conclusion I desire to state that my best
thanks are due to Professor Thomson for the advantages that
have been derived from his very valuable suggestions.
Monday, 22 February, 1897.
Mr F. DARWIN, PRESIDENT, IN THE CHAIR.
The following were elected Fellows of the Society :—
A. Liversidge, M.A., Christ’s College.
H. C. Robson, M.A., Fellow of Sidney Sussex College.
The following, having been nominated by the Council, were
elected Associates:
S. W. Richardson, Trinity College.
H. F. Hyndman, Trinity College.
|
i
1897. ] Mr Mayall, On the Diffraction Pattern ete. 259
The following Communications were made to the Society :
(1) On the Diffraction Pattern near the Focus of a Telescope.
By R. H. D. Mayatt, M.A., Sidney Sussex College.
The problem here considered is the diffraction pattern formed
by the light from a star on a screen placed near the focus of a
telescope. The exact theory of the diffraction of light through a
circular opening has been developed by Lommel, in his well-known
memoir on the subject*. It will be convenient to give here the
general conclusions at which he arrived, as applied to the case
under consideration.
If 6 be the distance of the screen from the focus measured
towards the object-glass, f and r the focal length and radius
respectively of the object-glass, € the distance of any point on
the screen from the centre of the image, and if we use the
abbreviations .
Haat 2a or? wean
TS Cas ies a eset
the intensity of light at the point ¢ is
We Trt (=) aval
PG sya) ete
1
= BY ( U2 + UF?)
where = (2) Ji (z)- (2) J, (2) +... ,
-(a0-(
and U,= (2) J. (2) IZ) eee;
in which the J’s are Bessel’s functions with the usual notation,
and both series are continued to infinity.
Now 5 ( = 5°) expresses the ratio of the distance of the point
€ from the centre of the image to the radius of the geometrical
image, and is therefore <1 for points inside the geometrical
boundary and > 1 for points outside. Hence for points inside the
geometrical image the series U, and U,, although absolutely con-
vergent, are not adapted to numerical calculation. They are
however related to two other series
Fes (=) a (-)— (2) Fe(e)+ the
Vi=Jo(2)—(Z) Sue) +.
* Abh. der Kon. Bayer. Akad. vol. xv.
260 Mr Mayall, On the Diffraction Pattern — [Feb. 22,
by the equations
ee gl Li
UL + V,=sing(y +7) 4
1 ae
— U,+ Vo=008 5(y ak
SU eae:
If - is not nearly equal to unity, i.e. for points which are not
2
far from the centre of the image compared with its radius, the
series V,; and V, are rapidly convergent and may be calculated
with ease from the tabulated values of the Bessel functions. They
were in fact calculated by Lommel for values of y equal to z, 27,
... 107, and for values of z from 1 to 12. But if = is nearly equal
to unity and at the same time y and z are fairly large, the cal-
culation would become extremely laborious, for the function J,
does not become negligible in comparison with J;, J,... when z is
large until 7 is also large, so that a great number of terms of the
series would have to be taken in order to get even a moderate
approximation to their true value. Now in the present case y
may be much greater than 107, even when the screen is very close
to the focus, thus if a= = the screen would have to be placed at
a distance of only about a millimetre from the focus in order that
the value of y should be so small as 107. And at the same time,
experiment shows that it is just when : is nearly equal to unity
that it becomes most important to determine theoretically what
the intensity of illumination ought to be.
A very interesting series of star-photographs has been obtained
by Mr Newall on plates exposed to the light of a star near the
focus of the large refractor at the Observatory. It appears from
these that when the light has been rendered as nearly as possible
monochromatic the image takes the shape of a bright ring sur-
rounding a darker space more or less uniformly illuminated. The
position of this ring is just about the boundary of the geometrical
image, and within it can be seen traces of one or two other rigs
but much inferior to the first im brightness. A great portion of
the light in the image is thus confined to the immediate neigh-
bourhood of the geometrical boundary, and as there is no reason to
suspect any excessive concentration of light there due to spherical
aberration, it 1s important to know whether the phenomenon is a
direct result of the undulatory theory of light or not.
An examination of the curves traced by Lommel, to represent
the variation in intensity of the light at different points of the
1897.] near the Focus of a Telescope. 261
image, gives no indication of any well-defined ring at the outer
boundary. It shows also no reason for thinking that, when the
values of y and z are larger than for those curves, the intensity
curve takes a kind of limiting form at its boundary which is
independent of the value of y, and yet this is certainly indicated
by the photographs.
In the following I have attempted to find an approximation, in
the general case, to the values of the series V, and V,; when y and
z are both great and their ratio nearly equal to unity.
Expressing J, (z) as an integral by means of the formula
()"s,(4)= | of cs? cos nd dd,
and writing 7 =x, where « <1, we have
Vi +1, =d, (2) + ted, (2) + Ped, (2) 4...
7
high? 2
=-| eos? (1 +x cosh+ x’ cos 26+...) db
0
— 1 i 4 — J
a 1—2« cos @4+x? ?
iz ( Ik =
——— iz COS ee See a
le {1+ —srepeatt
aes o i a as Z izcos® df : 1
Jo (z) + a [e We cae wk Wiad (1).
Now consider the integral
eee p dh _
0 fb — COS h
If w> 1 it may be expanded in the form
1 uy . Ss Ss?
| oo paces ees Pras aad ) dd
be
0
Lid id? Df
esp Oo aS pe \ eircom g
Al ae dz! Be dat ire ?
7 € ae CL a
tie ta ae?
sow ) J, (2):
d” J, (z)
dz”
Since «>1 and can never exceed a certain finite
262 Mr Mayall, On the Diffraction Pattern [Feb. 22,
quantity, the series above are absolutely convergent. The last
line is what we should obtain by integrating by parts the integral
lo.)
mre | GUE Sh) Ole
z&
Hence we have
he eizcos “eco = init | Cuan (z) dz,
0 zz
—cos
and polite =p In (1) it becomes
Vi.+1Vi,== sIe(2) +4 ao | GEAR AVC seed ()
in which «, and therefore p, are nee equal to unity, while z is
large.
To get an approximation to the value of the integral on the
right-hand side of (2) we may use the approximate expression
for J)
J(2z) = Nee _ [60s (Z-2)- = sin G- ‘) ;
with which value the integral becomes
of z i: oie cos (7-4) — a sin c — :)| = Lee (3).
This may be expressed in terms of Fresnel’s integrals
JP = | " cos aydy, Q= | "sin i wydy,
0 2 0 2
the values of which have been tabulated by Gilbert* from v=-01
to v=5°5. For we have
cE e7#* Gos G- A ws =s/ es} Cedi (Ge Ne dz
1 co de NS pe. dz
—=—¢ GOR tes | —t(w-I)z (A).
2 z Veo oe NE (4)
If we neglect terms in z* the first of the integrals in (4) is |
eg sun
— 5 te eHO#/(u + 1) ve
* Mem. couronnés de VAcad. de Bruxelles vol. xxxt.
1897. ] near the Focus of a Telescope. 263
while the second is
in (a)
a
= dz
5° i {eos (u—1)2—isin (n= 1) | &
ey es “(08 5 isin a,
=> rare a7 my” | dy
(where y=, [27 H— 22) a ope (5)
T
ee Boy eS ae)
The ratio of the first integral in (4) Ni the second is therefore of
— 1-
the order ni a : , Le. of the order 7a , So that the first integral
‘4
may be neglected. We have then approximately
MG el af On (lL 5 fl fy
[ee cos (7 2) <= 58 J cat s-P-*(5-@)|
=~ poy a/ 9 i -P-+P-ah.
The rest of the integral (3) is of an order which has already been
neglected. Hence, by substituting the value of (3) in (2), we have
approximately
ae Vis vie eins es abe ot.
ae
giving
Vo=s Sole go"
Ane |
\a — P—Q)sin pz — (P — Q) cos ue} :
(ul = P—Q)eos ue + (P= Q)sin pe}
1l+«
An/K
or, since U, = sin pz — V,, U.= V, — cos pz,
a
U,=| marl -P-Qh ran “ile mee
W=5 (1 4, ka-P- Q) cos “z+ 1 g(P-Qsin pe
264 Mr Mayall, On the Diffraction Pattern [Feb. 22,
and the intensity of light at points of the image close to the
geometrical boundary is given by
el = (UB A Ue
“fi Fga- rol fge-o}
— J, (z) {1 - Tieti-P- 0) | cos we ve (P= Q)sin pe | ;
This may be still further simplified, for (1 + «)/4/« differs from 4
by ;;(1—«)? when « is nearly equal to unity, and the error in
&°M? produced by putting « = 1 in the squared terms is
gg (1 — «)? (2P? + 2Q? — 1)
or about j,(1—«) at the greatest, while the error in the J, (2)
ee ee
term would be of order ve RIG
We have then M?= M? +e,
where eOMe=t(14+P4+Q0r+(P=- Qy]
and Se=—4J,(2) [1+ P+ Q) cos wz —(P— Q) sin wz].
It appears from this that the variation in the intensity of ilumi- |
nation consists of two parts, one of which J/,? represents all the
main features in the variation, the other being a small correction
of irregular form to be applied to it.
For points outside the geometrical boundary, M? takes a
different form. Here «>1 and
iU,— U=t9 F (2) +? (2) J, Qa.
2 1 feo (= @ if cos 2w 4 ...) de
0
2
K K
= {" &: K COS wa — 1
= — et COS w
TJ 0 1—2Kcos@a+x
ea iraes: e—1
BLS ha izcosw {__ ] 7
2Qar ay +75, ceo
1 Ke ie da
== = Jf, | iz COS w
2 o(2)+ Qar ip 1 — 2% cos @ + K?’
1897. ] near the Focus of a Telescope. 265
which as in the preceding case may be reduced to
< an 1 2 l+« oe 2) eae 5 i} ape
iU,— T= 5 Ju(2)+ gig {1-P-Q-1(P—Q es,
giving
U,= iin ia — P—(Q)sin pz —(P — Q) cos pel
ie aie (z) — ‘ne \a — P—Q) cos pz + (P — Q) sin ps}
and pe a
=3(1-P-Qr+(P-Oy
4 J.) (= P— 0) cospe + (P— Q)sin ps}
or We Moe,
where O'M2=}{1-—-P-—Qy+(P-Q)y}
Be’ = — 4. Jy (2) (1 — P— Q) cos we + (P — Q) sin ps}.
The values of M? and M,? may be calculated from Gilbert’s
tables for P and @: it will be remembered that the argument in
this case is
7
- /—
“Dy
the upper sign being taken in M,? and the lower in M,2, so that v
is proportional to the distance of the point of the image considered
from the geometrical boundary. The curve in the figure represents
&M? and 3M, for different values of the abscissa v, the origin
corresponding to a point on the geometrical boundary and
v= 4/2
YEP
to the centre of the image. The numerical values of 6°? and
&’M,? are given in Tables I. and II. The figure shows that the
intensity mcreases from zero outside the boundary until it reaches
266
0-1
0.1
G1
0.6
GG
0.6
G.§
0-7
GF
0.g
Mr Mayall, On the Diffraction Pattern [Feb. 22,
H
LS) C—~ for) co > i} J
° S S r—) = S S
Geometrical |Shadow
Bee
aS
‘Ber
r\
V/
As
Viet
Tae eee
1897.] near the focus of a Telescope. 267
its greatest maximum between v=1:2 and y=1°3 which will be
within a small fraction of the radius, it then diminishes to its least
minimum between y=1'8 and 1:9. Afterwards it passes through
a series of maxima and minima until at length it becomes practi-
cally constant and equal to unity. The appearance on a screen
would be that of a bright ring surrounding a series of fainter rings,
within a very small distance from it, these latter rings gradually
disappearing into a uniformly illuminated space. The outer ring
would be most conspicuous, not only by reason of its greater
intensity but also because of its greater width. On a photographic
plate exposed with a view to showing the existence of this outer
ring the probability would be that the light from the inner rings
would hardly affect the plate at all; in any case the maxima and
minima would be so close together and differ so little from each
other that they would be indistinguishable, except perhaps the
first two or three. Moreover, unless the light used were of a
single definite wave-length, the maxima and minima for different
wave-lengths would overlap. If the light were confined to a small
portion of the spectrum, this might not affect the outer ring very
much, since it is separated from the next inner ring by a wider
and darker interval than exists between any of the others, but a
very small range of wave-length would be sufficient to fill up
nearly all the other minima.
The curve J? only represents the variation of the intensity for
points which are near the outer ring in comparison with its radius,
for points nearer the centre the terms which have been neglected
would become more and more appreciable until the regularity of
the curve was entirely destroyed. These terms were of order
js (1 — «)? (2P? + 2Q— 1), and 1/Vz, of which however the first is
always small, since P and Q become ultimately equal to 4; even
the second would not make much alteration in the shape of the
curve unless z were as small as 100, so that the curve will represent
the intensity for a considerable distance towards the centre when
y is large. At the centre itself, as is well known,
82M? = 4 sin? 7 !
or the intensity varies with the position of the plate from zero to
4. From the centre outwards the intensity varies irregularly
until 1 — « and 1/7z become small enough to allow the application
of the preceding results.
The figure (Fig. 2) gives some idea of the shape of the intensity
curve from the edge of the image up to the centre, the variation
near the centre being quite irregular in the sense of varying rapidly
with the position of the screen, while the constant-part and the
variation at the edge are the same for all positions of the screen so
ViO lex ET Vi 21
268
long as it is far enough away from the focus of the telescope to
Mr Mayall, On the Diffraction Pattern
make y large.
1:00
1:10
2:00
‘7760
0365
6234
6863
7135
6975
6386
5492
“4509
3734
3434
_ TABLE I.
ei? v
2551 2°]
2602 || 2:2
2655 || 2:3
2708 || 2:4
2763 || 2:5
2819 || 2:6
2933 || 2:7
2992 || 2:8
3052 || 2:9
3113 || 3:0
3372 || 3:1
3720 || 3:2
‘4102 || 3:3
‘4517 || 3:4
‘4966 || 3:5
5450 || 3-6
5968 || 3:7
6518 || 3:8
————————— || 339
‘7099 || 4:0
“7707
"8327 Ay
8983 || 4:2
9635 || 4:3
1:0286 || 4:4
1:0920 AB
| 11525 || 4:6
| 1:2088 || 4:7
1:2593 || 4:8
eee eS |e 7 1c)
1:3358 || 5:0
1:3696
13519 || 5:1
1:2803 || 5:2
1:1638 || 5:3
1:0274 || 5:4
8897 || 5:5
8018
7815
“8440
[Feb. 22,
1897. ] near the Focus of a Telescope. 269
TABLE II,
vy | dM? | »v | em? || » | a2 || v | seat?
05 | -2262 | -30 | 1382 | -55 | 0865 || -80 | -0563
10 | -2008 | -35 | -1255 | -60 | 0791 || -85 | -0519
15 | -1854 | -40 | -1141 || -65 | 0703 || -90 | -o479
20 | -1679 || -45 | -1039 || -70 | 0665 | -95 | -0443
25 | 1522 || 50 | 0948 || -75 | -0611 || 1-00 | 0411
!
(2) On the marks made by stars on photographic plates ex-
posed near the focus of a telescope. By H. F. Newatt, M.A.,
Trinity College.
The appearances presented by some photographs of stars
taken with the 25-inch visual refractor of the Cambridge Ob-
servatory in the years 1893-4 were described and illustrated in
a paper “On the formation of photographic star-dises” by the
present writer, in the Monthly Notices of the Royal Astronomical
Society, Vol. tiv. p. 515. In that paper attention was called to
the existence of a considerable concentration of light in the
boundary of the circle of diffusion for light of any wave-length ;
and I was led by a series of observations and experiments, which
gave much information as to the excellent performance of the
object-glass, to express the view that “it may be a straightforward
result in the theory of diffraction through a circular aperture,”
that this annular concentration must exist.
The extension of Lommel’s work (Bavar. Acad. Mem. 1886,
Vol. Xv., p. 235), which Mr Mayall was good enough to undertake
at my suggestion and has accomplished and described in the
preceding paper (page 259), shows that near the focus of a perfect
object-glass with circular aperture the circles of diffusion must
exhibit an intensification of light of any given wave-length near
the boundary. Mr Mayall has in fact found that the undulatory
theory accounts for just such an effect as my experimental results
led me to anticipate.
A few more observations, and also some photographs taken
since 1894, have only confirmed my view that whilst there are
signs of some slight outstanding spherical aberration in the
25-inch refractor, the main factor in the production of the rings
which I have measured in the star-marks obtained with special
exposures of photographic plates has been the concentration of
light near the boundaries of the circles of diffusion for different
colours.
21—2
270 Mr Newall, On the marks made by stars etc. [Feb. 22,
Of these photographs I propose only to speak of two. In the
taking of one of them, the aperture of the object-glass was re-
duced to 24 inches, and an opaque circular disc, 12 inches in
diameter, was suspended in front of the middle of the object-
glass, so that light was prevented from falling on the central
part. The telescope was then pointed to a bright star and a
photographic plate was exposed near the focus, at a distance
14 inches within the visual focus (ze. nearer to the object-glass).
The appearance on the plate, which was sensitive to the yellow
and green especially between 5900 and A 5200, is mainly due
to the light focussed at the visual focus; and the mark produced
consists of a circular disc, whose outer edge is brighter than
the average and whose central part—that which corresponds to
the obstructed part of the object-glass—is blank ; but round the
central blank the intensity of photographic action is greater than
the average. To put it in other words, the mark is a broad ring,
whose external radius is twice the internal radius, and the in-
tensity at the edges of the ring, both external and internal, is
greater than the average within the broad ring; moreover the
brightness of the internal edge is greater than when no ob-
structing disc is used. The excess of brightness of the internal
edge is the point to which I wish to call attention.
The second photograph was taken under similar circumstances
except that the obstructing circular disc was displaced from its
central position, and set so that its centre fell halfway between
the centre and edge of the full aperture. In this case also the
marks on the developed plate exhibit an intensification of the
light round the edge of what may be called the shadow of the
displaced disc.
In both of the photographs described there were several ex-
posures of various durations on each plate. The effect of long
exposures is to obliterate the differences of intensity in different
parts of the marks. If the exposure is so short that the plate
is barely affected by the average intensity, then the parts where
the intensity is greater are seen with exaggerated distinctness.
It is easy to pick out amongst the various marks made with
different exposures, one or more that show the ring very
plainly.
The features seen in the photographs suggest the idea that
the intensification of the light near the boundaries of these
star-marks is a result which is to be expected with an object-
glass of any shape of aperture, whether circular, square or tri-
angular.
[Some photographs lately taken with a triangular aperture
show that this expectation is realized in fact. The triangular
marks are bounded by edges of which the intensity is greater
1897.] Mr Newall, On the marks made by stars ete. 271
than the average intensity within the boundary. Note added
1897, Mar. 15.]
The effects of spherical aberration would be distinguishable
from the diffractional intensification near the boundary by the
fact that the aberration effects would be different inside the
focus from those outside the focus, but the diffractional effects
would be the same on opposite sides of the focus.
(3) Theorems on the contacts of spheres. By Mr W. M°F. Orr,
M.A.
Few, if any, of the following theorems are new. Theorem (1)
is equivalent to the well-known theorem that all the generating
spheres of one system of a cyclide touch all the generating spheres
of the other system. Theorem (5) is proved analytically by Casey
(Proceedings Royal Irish Academy, Vol. 1x.). I believe they are
not generally known, however, and it may be worth while to bring
them together.
1. The problem to describe a sphere touching four spheres
may admit of an infinite number of solutions. For any four
tangent planes from a point to a sphere are touched by an infinite
number of spheres; by inversion from any point the four planes
become four spheres touched by an infinite number of spheres.
2, Any two spheres and their inverses with respect to a third
are touched by two infinite families of spheres. For if A, B be
two spheres and d’, B’ their inverses with respect to another
sphere O, the spheres which touch A and A’ are divided into two
families each doubly infinite, all the members of one of which
eut O orthogonally. Any sphere of this family which touches B
must therefore touch B’ and belongs to one or other of two singly
infinite families according as the natures of its contacts with A
and B are the same or different.
3. Any three spheres and their inverses with respect to a
fourth are touched in common by eight spheres and in general
by no more. For if A, B, C be three spheres and A’, B’, C’ their
inverses with respect to another sphere O, of the sixteen spheres
which can be described touching A, B, C, A’ (in case the solu-
tions of that problem are determinate), eight cut O orthogonally
and therefore touch B’ and C’.
4. The sixteen spheres which can be described to touch four
given spheres (in case the solutions of that problem be determinate),
consisting of eight pairs of conjugates, the members of each pair
being inverse to each other with respect to the sphere orthogonal
to the original four, any two pairs of conjugates are touched by
two infinite families of spheres. This follows from theorem (2).
272 Mr Orr, Theorems on the contacts of spheres. [Feb. 22,
5. Inthe same case any three pairs of conjugates are touched
by four spheres besides the original four. This follows from
theorem (3).
6. In the same case if the original four spheres be A, B, C, D,
the four pairs of conjugates which belong to the same doubly
infinite family touching any two of the given four as A, B are
touched by two other spheres besides the original four, namely, the
inverses of C, D with respect to one of the spheres of similitude
of A and B. This is obvious as the eight spheres mentioned,
touching C and D and cutting the sphere of similitude orthogo-
nally, must touch the inverses of C, D with respect to that sphere
of similitude. In this theorem as in the last we have a group of
eight spheres touched by a group of six.
(4) Change of the independent variable in a differential
coefficient. By E. G. GAtuop, M.A., Gonville and Caius College.
[This paper will appear in the Transactions, Vol. XVI.
Part II.]
Monday, 8 March, 1897.
THE PRESIDENT, Mr F. Darwin, IN THE CHAIR.
The following Communications were made:
(1) On the wyection of the intercellular spaces occurring wm
the leaves of Elodea during recovery from plasmolysis. By the
President, Mr F. DARWIN, and Miss D. F. M. PErtTz.
Hlodea continues to assimilate in salt solutions strong enough
to plasmolyse the cells. On replacing the plant im water assimila-
tion ceases, the gas disappears from the intercellular spaces, and
the leaf is mjected with water. The disappearance takes place
partly by the escape of bubbles at the open ends of the inter-
cellular spaces, but chiefly by solution. The first of these
phenomena depends on the surface tension of salt solutions being
greater than that of water. The authors are not able to explain
the solution of the air in the intercellular spaces.
1897.] Mr Blackman, The phenomena of Carbon Dioxide etc. 273
(2) The phenomena of Carbon Dioxide production associated
with reduced vitality in plants, By Mr F. F. BLACKMAN.
By the aid of an apparatus (which was exhibited), specially
adapted for physiological research on very small outputs of carbon
dioxide, several new phenomena of this nature have been brought
to light in plants.
These comprise the liberation of carbon dioxide produced in
the following four cases. Firstly, that resulting from the action
of temperatures between 40° C. and 50° C. on dry resting seeds :
at temperatures below 40° C. no appreciable formation of carbon
dioxide takes place, and at continued higher temperatures the
amount, which is at first large, does not remain so but steadily
falls off, indicating the decomposition of a definite limited quantity
of some substance. Secondly, the large amount of carbon dioxide
produced in the first few hours after wetting coarsely ground dry
seeds. This cannot be attributed to the action of micro-organisms
and is hindered by the action of chloroform and other poisons.
Thirdly, the varying production of carbon dioxide by the action
of volatile poisons and of fatal temperatures on living leaves.
Finally, the post-mortem production of carbon dioxide brought
about by subjecting recently killed leaves to the action of a
temperature of 100° C. This amount was shewn to vary with
the method of killing adopted, and evidence was forthcoming to
shew that in this, as in the other cases, these substances which
easily oxidise with liberation of carbon dioxide are in some way to
be associated with normal respiratory processes.
(3) On the leaves of BENNETTITES. By A. C. SEWARD, M.A.,
St John’s College.
In the second volume of the British Museum Catalogue of
Wealden plants!, I brought forward evidence in favour of including
Williamsonia gigas Carr., Williamsonia Carruthersi Sew., and
other species in the same family or even genus with the Lower
Cretaceous Bennettites. Although we have not as yet discovered
any example of Walliamsonia gigas showing internal structure,
there are many reasons for believing that this Lower Oolite fossil
represents an inflorescence very closely allied to that of Bennettites
Gibsonianus Carr. The immediate purpose of this article is,
however, to bring forward evidence in support of the somewhat
discarded view that Williamsonia gigas is the inflorescence of the
plant which bore the pinnate fronds known as Zamites gigas L.
and H. It is by the gradual accumulation of facts and the cor-
relation of various observations, that we are occasionally able to
1 “Catalogue of the Mesozoic plants in the Department of Geology” (Brit. Mus.)
The Wealden Flora, Part ii. 1895, p. 134.
274 Mr Seward, On the leaves of BENNETTITES. [Mar. 8,
surmount the difficulty presented by the almost constant occur-
rence of plant fragments as isolated and imperfectly preserved
fossils. We are now in possession of most of the data as to the
essential features of the Bennettitean mflorescence, but we have
hitherto had no satisfactory proof as to the nature of the vegetative
organs which were borne by Bennettites.
The juxtaposition of plant fragments in the same rock cannot
as a rule be accepted as evidence of much value. There is no
more serious difficulty in paleeobotanical work than that of piecing
together detached portions of the same species, and the isolation
of members of one individual has given rise to a multiplication of
generic terms which, though a matter of necessity, has been a
source of no little confusion. Anyone at all familiar with the
method of occurrence of Williamsonia gigas in the Jurassic beds
of the Yorkshire coast must have recognised its almost constant
association with Zamites gigas. The association is so frequent as
to naturally suggest an original union of the two fossils m one
plant. In the classic work by Young and Bird—A Geological
Survey of the Yorkshire Coast—published in 18221, a portion of a
Zamites gigas frond is represented in Plate IT. fig. 2, and in fig. 6
of the same plate we have a typical example of Williamsonia.
The authors do not give a name to either specimen, but express
the opinion that “figs. 2 and 6 appear to belong to one plant; the
former being a leaf, somewhat imperfect, and the latter the head
or fruit of the plant?” Bird’s drawing of the frond does not do
justice to the specimen which is fairly well preserved, and represents
a perfectly characteristic example of Zamites gigas. The original
fossils figured in Young and Bird’s work are preserved in the
Whitby Museum. The late Prof. Williamson devoted a consider-
able time during the earliest years of his scientific life to the
investigation of the fossils to which Carruthers gave the name
Williamsonia. No one has had opportunities of studying this
genus as it occurs in the rocks near Scarborough equal to those
enjoyed by Williamson ; and it is interesting to find that the most
recent work has tended to support many of the conclusions arrived
at by this observer. As early as 1834 Williamson’ expressed the
opinion that Zamites gigas was connected with Willamsonia, and
in his very able paper, published in 18704, this author is confirmed
in the view of the organic connection of these two sets of fossils.
This opinion was also shared by Brongniart®, who received an
1 Young, H. and Bird, J., A Geological Survey of the Yorkshire Coast, Whitby,
2 Ibid. p. 183.
> Geol. Trans. [2] Vol. v. p. 230, 1834.
4 Linn. Trans. Vol. xxvi. p. 663, 1870.
° Tableau Vég. foss. p. 62, 1849.
1897.] Mr Seward, On the leaves of BENNETTITES. 275
unusually fine collection of English Williamsonias from the late Mr
Yates. These specimens are now in the Natural History Museum,
Paris, and many of them were drawn for Brongniart with a view to
publication, but the work was unfortunately never completed. The
drawings were afterwards made use of by Saporta in his compre-
hensive work on Jurassic plants. In describing the Yates specimens
Saporta expresses himself strongly against the generally accepted
view as to the union of Williamsonia and Zamites. He does not
hesitate to separate the Zamites fronds from any connection with
the Williamsonias. There is he admits “une certaine conformité
apparente entre les appareils floraux auxquels on peut laisser le
nom de Williamsonia et le Zamites gigas, tel que le fait voir le
remarquable empreinte de la collection du Muséum de Paris (voy.
Pl.81, fig. 1). Nous avons tout bien de considérer les Williamsonia
comme représentant l’inflorescence d’une monocotylédone primi-
tive, révélant un type de Pandanées plus ou moins analogue aux
Yuccites, aux Podocarya, aux Holirion de Andrae, ete.’”
It is unnecessary to quote the various views advanced by
different writers as the botanical affinity of W2llcamsonia, especially
as these were in many cases largely influenced by Saporta’s
decision as to the complete independence of this genus and Zamites
gigas. Nathorst proposed a comparison of Williamsonia with the
Balanophoreae?, but afterwards* reverted to the opinion of the
earlier writers as to its connection with Zamites.
A recent examination of the Yates collection in Paris, and
a comparison of the numerous specimens in the museums of
London, Cambridge, Whitby and Scarborough has led me without
hesitation to regard the pinnate Cycadean fronds of Zamites
gigas as the leaves of the plant which bore a Williamsonian
inflorescence.
One not infrequently finds a small bud or young Williamsonia
borne on the end of a peduncle about 20 or 30 cm. long and 3 to
5 em. broad. Such an axis is covered with linear lanceolate scale
leaves spirally disposed and often clothed with delicate hair-like
ramenta, such as occur on the scale leaves of Dioon and other
recent Cycads. Such a peduncle is figured by Saporta on Pl. XV.
of Vol.iv.t The original is in the Paris Museum; the scale leaves
are less prominent and not so thick as those shown in the drawing,
and in this and other specimens one sees traces of the ramental
appendages. The best example of a peduncle is included in the
series of specimens of Wualliamsonia now in the possession of
Mrs Crawford Williamson, to whom my thanks are due for an
1 Pal. Frang. Plantes Jurassiques, Vol. 11. 1875, p. 55.
2 Ofr. k. Vet.-Akad. Forh. 1880, No. 9, p. 33.
3 Ibid. 1888, No. 6, p. 359.
4 Pal. Franc. Plant. Jurass. Vol. tv. 1891.
WAOIGS IDG aie 22,
276 Mr Seward, On the leaves of BENNETTITES. [Mar. 8,
opportunity afforded me of examining the fossils figured im Prof.
Williamson’s valuable memoir.
Saporta alludes to the resemblance of the pedunele which he
figures to the stem of Zamites gigas represented in his volume on
Cycads, Pl. XI. fig. 1, but does not regard the similarity as evidence
of relationship or identity. This specimen of Zumuites referred
to in the above quotation from the second volume of the Plantes
Jurassiques, is of exceptional interest and furnishes the most
important lmk in the argument in favour of the connection
between Williamsonia and Zanutes gigas. The figure in Saporta’s
work is very imperfect and conveys but a poor and erroneous idea
of the actual specimen. At the base we have a stem about 5 cm.
broad with the surface features indistinctly preserved, but showing
a number of imperfect scale leaves. To one side of the stem,
5 em. from the bottom of the specimen, are attached the petioles
of two clearly preserved fronds of Zamutes gigas, and above these
occurs part of a third frond apparently in its natural position but
without the petiolar attachment. The stem is prolonged obliquely
upwards to the left in the form of a branch about 3 cm. broad
and 14 cm. long. This branch is thickly clothed with hairy leaf
scales and terminates in numerous spreading leaf scales of a
narrow linear lanceolate form. The position and surface features
of this branch are very inadequately and incorrectly reproduced
in Saporta’s figure. If we now turn to the specimen figured
by the same author as a peduncle of Wzallaamsonia’, and which
terminates in what appears to be a closed Wilhamsonian inflor-
escence, we find the characters are identical with those of the
branch of the stem bearing Zamites fronds. Specimens of
peduncles in the British Museum, and others in the collections of
Whitby and Scarborough, afford similar proof of the identity of
the detached peduncles and the obliquely placed branch of the
leaf-bearing stem. There can be little doubt that the terminal
bud-like structure on these peduncles is a young and unexpanded
Williamsonia, but even if this be disputed, there can be no
question as to the identity of the typical Williamsonia scale leaves
and those of the terminal bud on the peduncles.
A specimen in the Whitby Museum shows a stem bearing two
diverging peduncles, and evidence of the same habit of growth is
afforded by an example in the British Museum. In all probability
the stem figured by Saporta (Plantes Jurassiques, vol. 11. Pl. XI.
fig. 1) bore another peduncle in addition to that shown in the
figure; this is suggested not only by the examination of other
specimens but also by the oblique position of the peduncle which
1 Pal. France. Plant. Jurass. Vol. 1. p. 55.
? loc. cit. Vol. Iv. Pl. xv.
1897.] Mr Seward, On the leaves of BENNETTITES. 277
is not brought out in the figure. The restoration of Zamites given
by Williamson in his well-known paper (Pl. 53)! accurately
represents what I believe to have been the manner of attachment
of the inflorescence and foliage leaves to the main stem.
The above description must necessarily lack completeness in
the absence of figures, but it is intended to publish drawings in
a monograph on British Cycadean plants now in preparation for
the Paleeontographical Society.
The precise relation between Williamsonia and Bennettites
must be left for future discussion, but evidence is not lacking in
support of the view that the two genera are both members of the
same family, and if not included in one genus they must at least
be placed in the same family of Bennettiteae. In the title to this
paper I have used the term Bennettites in a wide sense as includ-
ing plants of the Bennettitean type, though possibly generically
distinct.
The generic name Williamsonia, as expressing a more complete
knowledge of the botanical affinity of the fossil than the provisional
and comprehensive term Zamites, should be substituted for the
latter in the case of Lindley and Hutton’s species, Zamites gigas.
I am indebted to M. Renault for the opportunity of examining
the specimens in the Paris Museum and for permission to have
some of them photographed. My thanks are due also to Mr
Newbitt of Whitby and Mr James Rowntree of Scarborough, for
enabling me to examine the interesting examples of Walliamsonia
and Zanutes in the museums of those towns.
1 Linn. Trans. Vol. xxv1. 1870.
PROCEEDINGS
OF THE
Cambridge Philosophical Society.
On Ine’s Solution of a Partial Differential Equation of the
First Order. By A. C. Dixon, Se.D., Trinity College.
§1. The present paper gives an account and a proof of Lie’s
method* of solving a differential equation in one dependent and
any number (including unity) of mdependent variables. The
arrangement of the proof is such as to facilitate the examination of
certain cases of exception. Such are afforded by the tac-locus and
cusp-locus of the ordinary theory with one independent variable,
and their analogues, and also by an extensive class of equations in
which the linear partial form is included, and the integration of
which has been discussed by Mayer+. Notes are added on the
nature of a complete primitive, the complete solution of the
auxiliary linear equation, and the satisfaction of limiting conditions.
Method of Solution.
§ 2. Let z be the dependent variable, 2,, 2...a, the inde-
pendent variables and p,, p.... p, the partial differential coefficients
of z. If u, v are any two functions of these 2n+1 quantities,
denote the expression
r=n O(u,v) 7TS™ O(u, v)
ne 0 (2, Pr) iu aaa Pr 0 (2, Pr)
by the symbol (wu, v).
* See Forsyth, Theory of Differential Equations, Part I. pp. 238—9; or Lie,
Math. Annalen, Vol. vu. p. 242.
+ Math. Ann. Vol. vi. pp. 313—8.
VOU. 1x, PL. VI. Ze
280 Mr Dizon, On Ine’s Solution of a Partial
Then we know that the integration of any partial differential
equation
Ff Gig Os 2 2ny 25 Dis Pas >< Pn) =O eee eee
depends on the solution of the linear equation
CPD) S10 t ces seanseenah oe eee (2)
for @ in terms of a, ... %n, Z, Pi --- Pn. ‘The general solution of this
linear equation is derivable when that of the equation f=0 is
known.
§ 3. With regard to the expression (f, ¢) two things are
noticeable. In the first place it 1s indifferent whether we do, or
do not, suppose that wherever p,, say, occurs in ¢ it is to be
regarded as a known function of the other 2n variables, defined by
the relation f=0. This is true for each term in the expression
and therefore for the whole.
Secondly, the following relation holds
(u, (v, w)) +(v, (w, u)) + (w, (u, 2)
ou du ow
=—(v, W) AB (w, A (u, v) ag (3).
Hence if u, v, w are all solutions of the equation (f/f, ¢) =0 it
follows that the ratios
(v, w):(w, uw): (u, v)
are also solutions, unless they are constants.
§ 4. If now we suppose p, to be defined as a function of
GP 36 big Fp f0n 500 {Opa
by the equation f=0, and therefore not to occur in ¢ except
apparently, the equation (f, ¢)=0, which is linear and homo-
geneous in the 2n derivatives of ¢, is satisfied by 2n — 1 independent
functions, say Uy, WU... Um 1, and the most general form of ¢ isa
function of these.
We take any such form, say w, and seek next a common
solution of the equations
(Ff, $)=9, (ch, $)= 0.
This must be a function of u,, u.... Uen—, such that
r=2n-1 od
= (tt, Ur) the 0.
The coefficients in this equation, or at least their ratios, are
functions of u,, U2... Wen Since they satisfy the equation
(f, $)=0.
1897.] Differential Equation of the First Order. 281
Hence the condition (m4, ¢)=0 gives a linear homogeneous
equation connecting
Op Op _ 0d
f As]
OU,” Og OUan—a’
the coefficients being functions of , w,... Uen+1. The full number
of independent integrals of such an equation is 2n—2 and w is
one of them; we may suppose without loss of generality that the
FESt ATC Uy, Us ... Uon—o-
The condition (w., 6)=0, when ¢ is a function of
Ulay lee ten
is similarly satisfied by 2n —4 forms of ¢ of which wu, is one and
the rest may be taken to be us, wy... Uen—s-
By carrying on this process we get a series of n expressions
Uy, Uy ... Un, functionally independent of each other and such that
ny 10) Cp Us) =O (Lo S— 1, A)
We are now to shew how the integrals of the equation f= 0
depend on the functions w,, w, ... Up.
du
Ox;
respect to x;, account being taken of the dependence of z, p,, po... Pn
upon Z;.
§5. Let us write for the differential coefficient of w with
Thus
Ox; 4 Ox; io 02 j=l On; ; Op; i
and
t=! (diy OUg Ag OUy\ sis 0 (Ur, Us) (dpi _ —
i=1 (ae Op: Ou ap) ar ~. O( pis Pj) \ aa, Ou
OT Nac, 5 Se ty 2. va enn erect (4).
Putting f in the place of u;, we have
Tit, OF
- = = bya AUP rarcreracatarte ecatetatter 5),
2 an ane 0 @=12%..2) (5)
since f = 0 by supposition.
The system of 4n(n+1) equations thus found is, in virtue of
the relation f = 0, an algebraical consequence of the system
which contains the same number of equations.
23—2
282 Mr Dixon, On Lre’s Solution of a Partial
§6. The n equations (5) offer three alternatives:
(a) U;, Up... Up are all constants ;
(B) U, Usp... Un are variable, but
(i, Uy +++ Un) _
@ (Chg Bh don Gp)
so that they are connected by one or more relations ;
(y) se =0 GI ea):
If we take (a) we may have an integral, the complete primitive,
which is the result of eliminating p,, p.... Pn from
f=90, h=G), Up =Ay... Un =p.
If we take (vy) we may have an integral, the singular solution,
which is the result of eliminating p,, p.... Pn from
f=0 On
Cin? GiDs Op),
For (8), suppose the relations to be m in number, namely,
OR Oh Oh aon Vine Oa Ib A 50 10) scosccscc0e- (6).
Then only n—m of the equations (5) are independent—from
(4) we may deduce that
S Mey ogi & dd; Our _ 9 (ie ak
vl ee
ran Gy ODs e s=1 Oats : Ops
Each value of 1 gives a set of n equations of which only n— m
are independent and by comparison with (5) we deduce the n — m
relations
of of of
Bp uenay a aGes QO). cas sheaeeeeee (7)
Of. of. Og
Opieit topes ODn
Od»
Bago moa
Om Om
By) Te ae
Tf (8) leads to an integral it will be the result of eliminating
Pr» Po++» Pn from f=0 by means of the n equations (6) and (7).
The equation has thus n—1 distinct types of general integral
1897.] Differential Equation of the First Order. 283
since m may be any of the integers 1, 2, ... »—1, and the com-
plete and singular integrals are extreme types for which m has the
values n and 0 respectively.
All solutions of the equation f=0 are included among those
thus derived from any one system of functions
Uy, Un «~s Un;
but the system of functions is by no means unique, as is clear from
their mode of formation.
§ 7. We may verify these solutions in the following way.
Considering z, p,, p.... Pn as functions of 2, a... 2, we have
at once, since f=0,
; s=n
gee Oh Sc ates Ah Gee ae
é
sie Geer s=1 02, Op
and also
ou; dz ou; *%=" dp, Ou; du; (" Se Pa
6, 2s 3 ‘ :
Oar, Oxy ° Oz sa1 OL, OP, Oi
Thus
r=n du; of = Hime oS Lae Ot S)
= an, 4 yn tt ie eS Pr)
8=n T=Nn dps 0 (uw, f)
SS pe Oty f) 5a),
= fas al 02, 0 (ps, Pr) ( .
and
Ly ce ) 0 (wi, Uj)
r=n (= Ou; = du; = = (U;, Uj) 2S Aaa say (2, Pr)
—/ r id,
Ae "Ses O(m, wy) (4a).
Ox, Op, Ox, * Op,
6&=) r=) 0a, 0 (Ps; Pr)
(In the double summations 7, s must be unequal.) |
The first term on the right-hand side in each of the equations
(5a) and (4 a@) vanishes, since f= 0.
Now let these equations be multiplied respectively by the
determinants of the matrix
| Of Ou, OU, OUn
| Op.’ Op,’ Op. Op, |
r=1
eee essere
284 Mr Dixon, On Lne’s Solution of a Partial
and the products added. We thus have on the right
dz Of, Urs Ua «22 On)
(in -) 0 (2, Drs Po +++ Pn)’
and on the left
du, du, dus dun | »
04,’ Oa,’ Oa, °° Oa,
of OU, Up OUn
Op: ? Op; ) Op, so000ad 00006 On,
of OU OUn
ap,’ an es ANE ete ant
In hike manner
(S-p ) 0 (fy Uy +++ Un)
Dip Fy) Oli ses fp)
= the same determinant with x, written for z, in the first row.
In these equations we may substitute for u,, w,...U, any n
independent functions of them, say ¢,, ¢.... dn, the effect being to
multiply each equation by the Jacobian
O(di, be... hn) x
@) (Dns Why one Qin)”
We thus have
(dz \ Cf bu bubs) _| 9 th db, didn
Crs Pr) OZ pin ee pn) Wariner Geel Gue.
of ody Opn
Op, 5) Op: eeoreeeoeces Op,
Of ody
4) 1D I Ope CO i i ea
Of od
Opn ) On ee ee
_* If the relations among wu, u,... u, expressed by (6) are such that they cause
this Jacobian to vanish for arbitrary forms of ¢,4,, ...¢,, then the equations (6)
met be satisfied doubly by these relations, and this state of things can always be
avoided.
1897.] Differential Equation of the First Order. 285
The right-hand side of this equation vanishes if the equations
(6) and (7) are satisfied, m being zero or any whole number up to
n inclusive. Thus in general the equations (6) and (7) give p, as
the value of a and therefore afford a solution of the differential
equation (1), which was to be proved.
The relations (6) with f=0 form a ‘complete system,’ the
singular solution of which is given by (7). Thus we may say that
all the solutions of f= 0 are singular solutions of complete systems
to which f=0 belongs. It is not necessary to form all such com-
plete systems in order to have all solutions.
Cases of failure.
§ 8. The proof will fail if
OULU ne tn)
Te En ie Te 8).
OZ} Dis '2.2 Dn) (8)
If we multiply the equations
Gia) —0; ete: -(%,,.1,) — 0, ete:
by the second minors of this Jacobian, formed by leaving out the
derivatives with respect to z and p,, and add, we have, as other
forms of the relation
O Cf, tis <<: Un) _¢
0 (2, Di ooo Dig) :
Fe We. 3.5 UR)
eat OG Diy. Dn)
Hence it follows that all the determinants of the matrix
| ef of OF 20f wOF Of ll some seeessehn
Gn Or, 0%, 02 “Op, Op, |
| Ou, Oy OU, Ou, Ou Ou,
Ct Crue Ol, 02 Op, | OD,
SUK oe Re) cacaetocce (9);
jn]
=
a
286 Mr Dizon, On Lie’s Solution of a Partial
vanish unless those of the matrix
Sp ee a Ne (11)
Op, : Op, of OD;
of Un
aps Vaan
are all zero.
There are therefore two kinds of exceptional cases, which we
shall now examine*.
§9. The equations (7) may be written
a Sn ae =(), G=Hil, Zs.)
Thus if (7) A i are both true it follows that
ot 0d;
ag Po Be
unless the determinants (11) vanish. In the same way from (9),
unless the determinants (11) vanish,
=),
of Odi
— . = = Dae ofl).
r An + Sy; Aa, O, (eal, n)
* The proof also fails if
O (brs Po -+- bn) _
=0
CNS hyaos CA)
that is to say, since $,,4;, ... , may be chosen arbitrarily, if
ee eee
Cite NOt rots ;
Bip, 7 Hopareesvone
Cbm Ohm
ay, ose cies
These equations are n—m-+1 in number, and as u,...u, already satisfy the
m equations (6) they will generally be inconsistent. If however any values satisfy
them they will also satisfy (7). If the values are isolated then these relations
afford a solution which is included in the complete primitive, since the values of
U,...U, are given. If the values are not isolated then these relations are not
numerous enough to enable us to eliminate p...pp-
1897.] Differential Equation of the First Order. 287
The values satisfying these conditions will occur twice in
the oo *-™ determined by the m+1 equations (1) and (6) in the
2n +1 quantities 2, ...%p, 2, Pi -+- Dn-
Thus if (8) is not a new relation this o”-”" must contain a
double «”*, which will satisfy (7) but not be a solution of the
differential equations (1) and (6). Any complete primitive of
the system will define an «” on the «”~” and it will not
generally happen that a complete primitive will, in geometrical
ag meet the double o” in the same point on both
sheets.
The system of values of a,...%n, 2, Pi» Pn Will therefore
be common to two complete primitives, which thus have contact
with each other, so that the complete primitives of the system (1),
(6) have a tac-locus. This is one of the cases of failure.
The second is that in which the determinants (11) all vanish
in virtue of a single relation. This relation will clearly be
included in (7), at least as an alternative, and the other alter-
native, if any, must be taken in order to find the singular solution
of the system. In this case the complete primitive 0” has an
"1 of cusps, that is of points where 2, ... #,, 2 are all the same
for two consecutive points. The cusps of the system (1), (6) will
form an o?—"—1 within which the equations (7) define an 2”.
This will generally not satisfy the differential equations.
The occurrence of a cuspidal ©” on the complete primitive
ought perhaps to be considered as normal, since generally the
vanishing of the determinants (11) will be secured by the
vanishing of a factor of the left-hand side of (8)+.
If we consider a singly infinite series of complete primitives
of (1), regarding only the "+1 (z, a,,... #,), each primitive has
the cuspidal oo” as part of its intersection with the consecutive.
If we consider a doubly infinite series then each primitive has
an 0” of points on the cuspidal x” as part of its intersection
with two consecutives, and so on. Thus, whatever the value of
m (<n) in (6) there will be an o” of cuspidal values satisfying
(1), (6) and (7) algebraically but not generally satisfying (1) and
(6) as differential equations.
§10. The condition (8) is satisfied also by the vanishing of
any factor that occurs to a higher power than the first in any
* Possibly the double systems may form a manifoldness of more than n
dimensions. In such a case the equations (1), (6), (7) will be satisfied by an
arbitrary ©” contained therein, but in general this will not be a solution,
+ For instance, take the equation z=p,%,+p.%).+p,p.- It has any number of
complete primitive forms, representing different doubly infinite series of developable
surfaces, and it is only in exceptional simple cases that a developable surface has
not a cuspidal edge.
288 Mr Dizon, On Lie’s Solution of a Partial
particular complete primitive. In such a case however the
solution does not fail as may be seen. The failure in general is
due to the fact that the first derivatives of the proposed solution
do not give determinate values of the derivatives of z, but must
be taken in combination with the second derivatives of the
proposed solution. From these, one or more equations have to
be formed involving only the first derivatives of z, and these
equations are not generally satisfied by the values p,, p, ... Pn-
If however for particular values of the constants an equation
of the form \?4 = 0 can be formed from the equations
of — Oe 6a — ys tn 1 na iy, 0, eee (12),
then, on the supposition that 7 =0, the relations found from the
second derivatives of 24=0 will be simply repetitions of those
found by removing the factor X from the first derivatives. The
effect will be the same as that of removing the factor X from the
final equations of § 7, and thus the results
d
aE filo (P= dh race)
hold under these conditions, and there is no failure.
§11. Another possibility is that the condition (8) may be
satisfied identically or in virtue of the equation f=0 only. Since
Uy, .-.Un are supposed independent, it is not possible for the
conditions (10) to be satisfied identically, and hence (11) must
hold good.
In this case the equations (12) give more relations than one
connecting 2, 2, 2... %, and therefore the supposition (a), (§ 6),
cannot be entertained. Let & be the number of mdependent
relations not involving p,, p.... Py that can be deduced from (12) ;
then in (6) we must suppose m not to be greater than n—k+1
or it will be possible to deduce more relations than one among
Z, @, @_...%,. Also the relations (7) will reduce to n—m—k+1
in number, /—1 being consequences of the rest, since the deter-
minants of order n —k + 2 formed from the matrix (11) vanish.
§ 12. The equations (4a) and (5a) now give, in virtue of (6)
and (7),
T=k / dz OCF; tas Uste-- Unesa) A
> ( Le ae
0x, aes 0 & Pr> Pk +: Pn)
and other such equations, each being linear and homogeneous in &
of the quantities
r=]
a Opie lair):
1897.] Differential Equation of the First Order. 289
But the relations (6) and (7) are now only n —&+1 in number
and therefore fail to determine 2, p,,...p, mn terms of a,... ap.
They may be taken as determining 2, px, Prii--- Pn in terms of
Ly, +++ Py, +.» Pea and it is then easily found that
dz
—= = .k-1
= ONG i.e 1),
dz _ _O(f, di, bo--- Gm), OF, Gis a =» Pm)
On, O(&;; Pr cpa) iMag (2, Pry 4D)
eS 12a. 2).
Thus the relations (6) and (7) yield an equation connecting
Z, %, ... ® and leave k—1 of the quantities p,, p.... Py, un-
determined.
If then we suppose py, 2... Px to have the values just found
for = (r=1, 2... &—1) it will follow from the equation (13) that
dz
Oa, 2
and in the same way
2 = pr (eas My bere n).
Thus we may say generally that the equations (6) and (7) yield
at least one relation among 2, #, ...#,, and when they yield only
one, that is when m}n—k+1, that one relation satisfies the
differential equation f= 0.
Exceptional cases may arise here, again corresponding to the
tac-locus and cusp-locus. In the one case all the minor determi-
nants of order n —k + 2 formed from the matrix (10) vanish, in the
other those of order n —k +1 formed from (11).
§ 13. We are thus introduced to classes of differential equations
in which certain of the forms of solution are wanting. Lagrange’s
linear equation is an extreme case, in which k=n. It is of course
the only case that can occur when n=2. In general the class
includes equations formed by eliminating the arbitrary constants
and function from an equation of the form
air (U1, Uz... UR) =0
where 2, v,... are known functions of z, 2... #, involving n —k
arbitrary constants, and y is an arbitrary function. The differential
equation is of such a form that it is satisfied by equating n-—k+1
of the quantities p,, p,... pn to linear functions of the rest, the
coefficients involving z, 2, ... #,andn—k parameters. For instance
290 Mr Dixon, On Ine’s Solution of a Partial
when n=3,k=2 the equation f=0 must so far as Pry Ps» Ps are
concerned satisfy the condition for a ruled surface. This is neces-
sary but not sufficient unless k = n.
§ 14. The number of complete primitives is unlimited, but it
should be noticed that not every solution involving n arbitrary
constants is a complete primitive in the sense that all other
solutions can be deduced from it.
It may be that an equation
I (G; Ghy Broce Gay Crecos Gn) =U
is such that from it and the n derived equations
OF oF
rag alien (GPs 1 AF ose 70)
two or more equations can be deduced in which the arbitrary
constants do not occur. Let these equations be
fra, jeS0 cope:
Then all the solutions derived from #’'=0 by the ordinary
method of variation of parameters will satisfy this system of m
equations, and therefore will not include all the solutions of any
one of the system, say f, = 0.
For instance the equation
DZ = A,X? + AX XL, + AzXe?
is a solution of
2 = PyLy + Pl. + P33 + Pi Peps
containing three arbitrary constants, but since it satisfies the
equation p,=0 also it is not a complete primitive in the true
sense.
§15. IZfany complete primitive of the equation f= 0 is known,
the general solution of the auxiliary equation (f, ¢)=0 can be
deduced * as follows.
Let JOA REAR Os ea ian hy, Oy oon Ca) 0)
be the complete primitive. Then from this equation and its n
derivatives expressions can be found for a,, a)... @», in terms of
Z, @...%n, P, -.. Pn; Otherwise it is not properly a complete
primitive. Let these expressions be mm, ww... Un respectively.
Then 2, %&s... Up, are n of the 2n — 1 solutions of Cid) 0)
Another complete primitive can be found by taking
An = a,b, + a,b, +... + An Dn— + bn,
* See Mayer, Math. Ann., Vol. vit. p. 311.
1897. ] Differential Equation of the First Order. 291
and eliminating a,... d, by means of the equations
oF oF
lage eas (r=1,2...n—1).
We still have a,=2,, d2= Uy... Gn =Un and the values of
b,, b,...b, are solutions of the auxiliary equation. Thus the
2n —1 necessary solutions of the auxiliary equation are %,, Uz... Un
and the ratios of
au aU a
Ou, ; Dus vee dun >
where U denotes
Dd CRF. ORE A oR) a
It is easy to shew that these are independent, and thus we are in
a position to write down the general solution of the auxiliary
equation.
$16. It would appear at first sight that the determination of
the forms of the arbitrary functions to satisfy limiting conditions
would involve the solution of differential equations, since the
derivatives of the arbitrary functions occur in the solution; this is
however not the case.
Suppose for instance that the value of z is given when 2, = 0,
say eS CRA Rens) }
The values of p,, ps... Pn are therefore given when «#, =0, for
then pra 2 (r=2,3...0)
These values may be substituted for 2, 2, p., ps... Pn mn the
equations
f= 0, U, =A, Ug= Ag... Un = An,
and the n quantities p,, 2... Z, may be eliminated.
Thus one or more relations will be found among @, a... dp
and these are what were required.
More generally if the solution is to include all systems of values
that satisfy the equations
Xi (z, DY, Loos Ln) = 0, X2 (z, Hy, Vz «+. Xp) = 0,
the values of p,, p.... Py, corresponding must satisfy the n—1
relations
—1, Pi, Po. Pn ||=9.
02 i OL Vor iin Ly,
a2? Da, oan
292 Prof. Anderson, On the Apparent [Apr. 26,
The elimination of z, 2... 2, P: --. Pn from these n —1 relations,
and
Vi = 9, %.=0, f= 0, wy =a «1. Un = An,
will give one or more equations connecting a,, a... d,, and these
are what must be used to derive the particular solution sought.
Monday, 26 April, 1897.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
The following were elected Fellows of the Society :
R. Lachlan, Se.D., Trinity College.
W. M. Coates, M.A., Queens’ College.
S. 8. Hough, M.A., St John’s College.
Rev. P. E. Bateman, M.A., Jesus College.
The following Communications were made to the Society:
(1) On the Apparent Electrification in an Electric Field at
the Bounding Surface of Two Dielectrics. By Prof. A. ANDERSON,
M.A., Queen’s College, Galway.
In Maxwell’s Treatise on Electricity and Magnetism, Vol. I.
3rd edition, p. 100, the apparent surface charge o’ on the boundary
of two media of specific inductive capacities K, and K, is defined
Poe aad ;
by the equation Te + ai + 4aro’ = 0.
Maxwell then proceeds to state, giving a reference to Faraday,
that if, durmg the action of the inducing force, the apparent
electrification of the surface be discharged by passing a flame over
the surface, then, when the inducing force is taken away, there
will appear a true electrification opposite to o’. In an Appendix
to the chapter in which this occurs the apparent electrification is
described as acting on the conducting flame which is in connexion
with the earth, attracting electricity of opposite sign, and repelling
electricity of the same sign, the consequence being the production
of a real electrification which masks the effect of the apparent one.
Prof. Gray, in his Absolute Measwrements in Electricity and
Magnetism, Vol. 1. p. 113, says that the action of the flame is to
reduce the surface to zero potential, and that the real electrification
is equal and opposite to the apparent electrification.
In Mascart and Joubert, Vol. 1. p. 101 (English edition), it is
stated that, though the layer of density o is a fictive layer, if its
surface is brought to the neutral state by means of a flame, and if
the sources of induction are removed, a real layer of density o will
be found on the surface.
1897.] Electrification in an Electric Field, ete. 293
Again, Wiedemann, in Die Lehre von der Elektricitdt, Band 11.,
asserts that the flame removes the apparent electrification o’, and
produces a real electrification of opposite sign depending on the
action of the apparent electrification on the interior of the body.
There seems to be some obscurity as regards what is meant by
removing the apparent charge. Prof. Gray, however, clearly states,
and I think the same thing is implied in the Appendix to the
chapter in Maxwell above referred to, that it means reducing the
surface to zero potential. It would, I think, be impossible to do
this unless for the portion of the surface affected by the flame at
one instant: if the flame be taken to another portion of the
surface the real electrification produced there will alter the
potential of all parts of the field and, therefore, of that part which
has already been reduced to zero potential. To reduce the whole
surface to zero potential, a flame large enough to affect all parts
of it at once would be necessary. But, if this is what is meant
by removing the apparent electrification, the real electrification,
as will be shewn presently, is not necessarily either equal in
amount or opposite in sign to the apparent electrification. Another
way of putting it, used by Mascart and Joubert, is ‘reducing the
surface to the neutral state.’ It is not clear what this means,
unless it be making the electric stress zero at every point of the
surface, on both sides of it. But this by Gauss’s theorem is
impossible if a real electrification is produced by the flame.
What seems to be properly implied by removing the apparent
charge is making the surface density of this charge, as defined by
Maxwell, zero; that is to say, a real charge must be given to the
surface which will make the normal force at any point of it
continuous. But, generally, this could not be done by means of
a flame.
Let o’ denote the apparent electrification, and o, the real
electrification necessary to remove the apparent charge. Also
let V denote the potential at any point before and V’ after the
apparent charge is removed, and V, the potential due to the real
electrification of the surface. Then, V’=V+V,, and we have
dv aV
dn, adn,
dV dV
gt May, 9
+ 47ro’ = 0,
d rrr
also Ha, Wt toe Maras Ct V,) + 4aro, = 0,
d d
an, V+ Vi) + ay V+ Vi) =0.
294 Prof. Anderson, On Apparent Electrification, etc. [Apr. 26,
Hence, Fea ie IU sail 1)
Ny Ane
GH, Gh, re
and dm + dn, _ 40a = 0.
To remove the apparent electrification is, then, equivalent to
finding the actual surface density o, of a distribution of electricity
on the bounding surface of two media of specific inductive
capacities K, and K, which would produce an apparent surface
density —o’, there being no other electricity in the field. This
problem admits, in many cases, of an easy solution.
As an example, consider the case of a charge e at the centre
of a sphere whose radius is a and specific inductive capacity K,,
the medium outside the sphere being of specific inductive capacity
Qe
paste
K, K,
iz = The surface density, o’, of the apparent
2
AS et inate wien 2
Inside the sphere the potential is ae +2 ( ip and
outside it is
: aL MA, é 1 1
electrification is, consequently, ree (Zz — =
To find the real electrification which will remove all apparent
electrification, we must find the distribution o, on the sphere which,
of itself, would produce an apparent distribution of surface density
e 1 1 a. : e KS
aia ‘z — mal This is easily shewn to be Fuse (1 — =) ;
and is, therefore, not equal to —o’ unless when K,=1. When
this surface distribution is placed on the sphere, the potential
both inside and outside is = , and the force is consequently the
1
same on both sides of the surface, as it ought to be when there is
no apparent electrification.
Suppose, on the other hand, we bring the surface to zero
potential by means of a flame. The potential at all points outside
will be zero, and the potential inside z (-- *). The surface
1
density of the actual electrification of the surface is, therefore,
- rant which is not —o’ and not opposite to o’ unless when
K,>K,. Besides, there is still an apparent electrification of
surface density — roayee
1
1897.] Mr Newall, On Luminosity attending Compression. 295
(2) On Luminosity attending the compression of certain
rarified gases. By H. F. Newatt, M.A., Trinity College.
1. Morrem (Pogg. Ann. 1862, Vol. 115, pp. 350—2, and 1865,
Vol. 126, pp. 643—654) and Sarasin (Pogg. Ann. 1870, Vol. 140,
p. 425) have given accounts of phosphorescence produced in
rarified gases by the passage of electrical discharges. The pheno-
menon itself was recognized in the earliest days of vacuum tubes.
Morrem and Sarasin agreed in thinking that no pure single
gas (as distinct from a mixture of gases) exhibits phosphorescence.
Morrem found the phosphorescence very strong in a mixture of
gases containing 200 parts of Oxygen, 100 parts of Nitrogen, and
150 parts of SO,. Sarasin regards the presence of oxygen as
essential to the production of phosphorescence. J. J. Thomson
(Recent Researches, 1893, p. 184) has described observations of
such phosphorescence and has explained it in accordance with
his view that the conduction of electricity by a gas is associated
with decomposition. He states, “I have never detected any glow
in a single gas (as distinct from a mixture) unless that gas was
one which formed polymeric modifications, but all the gases I have
examined which do polymerize have shown the afterglow.”
2. In the course of an investigation of the spectra of rarified
gases rendered luminous by electrodeless discharges by Prof. J. J.
Thomson’s method, I was dealing with the case of mixtures of
Oxygen with other gases, chiefly Nitrogen and Carbonic Oxide
in different proportions, and frequently obtained mixtures which
at certain exhaustions phosphoresced so brilliantly that I was
induced to devote some time to the study of the phenomena, in
particular by means of the spectroscope.
3. A description of the apparatus used will make the con-
ditions clearer.
A glass tube, in which electrodeless discharges were to be
passed, was connected with a Hagen-Topler mercury-pump, fused
glass joints being used throughout. There was also attached
to the pump a graduated tube in which mixtures of gases could
be made in any desired proportions, and which served as a
reservoir of such mixtures. Samples of the mixtures could be
let into the pump by an arrangement very similar to that figured
by Salet in his Traité de Spectroscopie (Masson, Paris, 1883),
p. 209. In most of the experiments the electrodeless discharge
was produced near the middle of a large tube, about 2 inches
in diameter and 6 feet long. In a tube like this the phos-
phorescence begins near the bright discharge and spreads along
VOL. IX. PT. VI. 24
296 Mr Newall, On Luminosity attending [Apr. 26,
the tube, in some cases quite slowly (about 1 foot per second),
in other cases too quickly for any estimate to be made without
special apparatus. The rate varies with the pressure and with
the mixture used.
4. The colour of the phosphorescence is very varied ; I find
among my notes that at various times the following colours have
been observed :—white, silvery-grey, yellow, yellow-green, old gold,
ruddy yellow, brilliant blue. The phosphorescence is undoubtedly
diffused throughout the whole volume of the gas enclosed in the
tube. There is an appearance of semi-opacity in the phos-
phorescent gas, except in the case of a certain brilliant blue
phosphorescence. The contrast in this respect between the
yellow and the blue afterglows is as marked as that between
a clear solution of copper sulphate and a liquid rendered turbid
by a slight yellow precipitate in suspension. The blue phos-
phorescence is marked, in my mind, as of an exceptional nature ;
I have only seen it four or five times, but it has generally been
of so short duration, that I have not been able to study it fully,
nor can I say what conditions are necessary for its appearance,
except that I connect it with oxygen and sulphur.
Spectrum of the phosphorescent gas.
5. A careful and long continued spectroscopic investigation
shows that the spectrum of the phosphorescent glows that I have
examined is a continuous spectrum. Prof. Thomson records the
observation of a few bright lines, if very high dispersion is used,
but I have been unable to corroborate this observation. (In
view of what follows in this paper, I should explicitly state that I
refer here to the spectrum of phosphorescence which has been
excited electrically in the rarified gas.)
6. An arrangement somewhat similar to a phosphoroscope
was used.
Between the spectroscope and the tube in which the phos-
phorescence was produced, a sector or sectors of a circle were
rotated by clockwork, which also drove a contact-break in the
circuit that produced the bright discharge in the tube. It was
arranged that the sector intercepted the light of the bright
discharge, and allowed only the light from the phosphorescent
gas to pass into the spectroscope. The spectra were observed
visually and were also photographed. Both methods showed a
continuous spectrum without any trace of bright lines, except on
one occasion to which I refer later (§ 27).
1897.] the compression of certain rarified Gases. 297
7. The spectroscopic study of the phosphorescence itself has
then given no evidence of its chemical origin. But the fact that
a continuous spectrum is visible in a gaseous mixture of such
tenuity as that dealt with (about 0™"3—0™™"1 pressure) is
noteworthy. I was unable to detect diffuse bands or a maximum
of brightness though the difference of the colours of the phos-
phorescent hazes in different mixtures of gas would lead one to
expect the existence of such bands.
8. The spectrum of the bright discharge which precedes the
phosphorescence has only given results difficult to interpret when
taken in connection with one’s knowledge of the care that has
been taken in preparing the gases.
For instance, a bulb had been carefully filled with electrolytic
oxygen, after ‘rinsing’ the pump and tubes out with the gas,
and after heating the tubes several times at very low pressure,
and after leaving the pump and tubes exhausted for two or three
days. The bright discharge gave only the band spectra of nitrogen
and cyanogen, and it was only after continued sparking that the
oxygen spectrum asserted itself.
It seems to me that the spectrum of the bright discharge
possibly affords no more certain evidence of the chemical origin
of the phosphorescence than of the nature of the mixture of gases
in which the discharge takes place.
9. The appearance of the phosphorescent gas led me to apply
a test, which Sir G. G. Stokes has described as affording proof of
the existence of solid particles in the flame of a candle. A beam
of sunlight was concentrated by means of a lens upon the phos-
phorescent gas: and the track of the beam in the gas, as also the
scattering of polarized light, were looked for. But no evidence
could be obtained that supports the idea that we might have to
deal with the phosphorescence of solid particles momentarily set:
free by decomposition accompanying the bright discharge.
10. In the course of my work with electrodeless discharges I
have frequently found black or brown deposits on the inside of
the glass tubes. In one or two cases the deposit has been thick
enough to form a film which could be detached from the glass;
the film was translucent and had a highly offensive smell. The
formation of this film is a proof that permanent chemical changes
are brought about by the discharge ; and there can be little doubt
but that the phosphorescence is a sign that temporary chemical
changes are also produced.
11. Taking into account the difference in the colour of
different phosphorescent hazes and the difference in the condi-
tions of their appearance, but setting only small weight on the
24—2
298 Mr Newall, On Luminosity attending [Apr. 26,
indications of the spectrum of the bright discharge preceding
phosphorescence, I am led to connect
white phosphorescence with mixtures contaiming oxygen and
carbon compounds,
yellow phosphorescence with mixtures containing oxygen and
nitrogen,
blue phosphorescence with mixtures containing oxygen and
sulphur.
Pressure conditions.
12. So far as my experiments have gone, the phosphorescence
appears in rarified gases between the pressures 0™6 and 0™™-01.
It rises in brightness as the pressure is reduced and reaches a
maximum at a pressure of about 0™™4, and fades away into
invisibility as the pressure is further reduced. These pressures
vary within small limits according to the nature of the gaseous
mixture.
13. To measure the pressure, the pump has been calibrated
in the well known method. The capacity of the pump-bulb is
close upon 500 ¢.c.; and the bubble of air in the exit tube, measured
at atmospheric pressure (or, at a pressure of one-tenth of the
atmospheric pressure when very high exhaustion is to be dealt with),
affords means of estimating the pressure of the permanent gases
in the vacuum tube connected with the pump. A careful set of
experiments on the indications of the gauge has shown within
what limits they are trustworthy if certain precautions are
attended to, the chief being that sufficient time should be given
for the equalization of pressure throughout the tubes and bulb of
the pump. Unless the connecting tubes are of large diameter the
time required, when the pressure is of the order of 0°:1—0°01, is
very great, something like 20 to 30 minutes, and it is consequently
probable that if the pump is worked at a rate greater than one
stroke in 20—30 minutes, the relative proportions in a mixture of
permanent gases will be altered considerably by the inevitable
differences in the rates of transpiration of the components. The
connecting tubes used in my experiments are about 2 yards long
and have an internal diameter of about + inch.
14. Striking effects may be observed if the pressure of the
phosphorescent gas be altered whilst the gas is actually phos-
phorescing after a bright discharge has been passed. Thus
suppose the pressure of the gas is higher than that at which the
maximum brightness for the given mixture occurs; then if
during phosphorescence the pressure is reduced, a wave of increased
brightness passes from the end of the tube near the pump to that
remote from it.
1897.] the compression of certain rarified Gases. 299
Pressure-glow, or luminosity accompanying compression.
Up to this point the present note deals with phosphorescence
excited electrically and I now turn to the observations which
suggested the title of the note.
15. The Hagen-Topler pump and tubes were filled with a
mixture of gases capable of exhibiting the yellow phosphorescence
that I attribute to oxygen with a trace of nitrogen in it. The
pressure was reduced below the value for which electrically excited
phosphorescence was a maximum for that mixture, namely below
o™™-4 or 0™"3. Then the gas in the bulb of the pump itself was
compressed in the usual process of pumping, preparatory to its
being driven out of the pump. As the compression proceeded, the
gas was observed to become luminous throughout that part of the
pump-bulb which was not occupied by the rising mercury. Its
brightness increased considerably and then gradually faded away.
The maximum brightness was enough to enable one to read
ordinary small print with ease. The amount of compression
necessary for maximum brightness was found to depend upon the
initial pressure.
16. After the gas has been compressed and has given out the
‘pressure-glow,’ then if it be allowed to return to its original
large volume and low pressure and be again compressed in the
pump-bulb, the gas does not glow, unless a certain operation has
taken place at low pressure; it consists in (i) lowering the
mercury in the pump-bulb enough to open connection between the
pump and the tube used for the electrodeless discharge, and
(ii) producing an electrical discharge in this tube.
17. It would appear that before compression the gas can be
put into a state of combination or grouping, which is stable at the
lower pressure; and when compression has raised the pressure to
a certain value, the original grouping of atoms or molecules is no
longer stable and the gas passes into a new state of grouping
with an evolution of energy, part of which would account for the
‘pressure-glow.’ In some way the electrodeless discharge supplies
the energy necessary to the formation of the combination which
is stable at low pressure. Inasmuch as the mixture of gases,
in which pressure-glow occurs, consists of oxygen with only a
trace of nitrogen (and possibly some other gases which would
_ ordinarily be treated as impurities), it immediately occurs to one
that we have to deal with the formation of ozone at the low
pressure. It is however not clear what part is played in the
phenomena by the impurities, though it seems certain that their
presence is of importance, if not essential for the production of the
phosphorescence.
300 Mr Newall, On Luminosity attending [Apr. 26,
18. With reference to the amount of compression necessary
for maximum brightness in the pressure-glow, a number of
experiments were made under varied conditions and the results
were found consistent with the idea that the maximum brightness
of the compressed gas occurred at a pressure between 0™"’5 and
0™"3, fairly definite for a given mixture of gas. If the initial
pressure of the rarified gas in the pump-bulb were small (eg.
0™"-01) the pressure-glow did not begin to take place with any
brilliance until such a diminution of volume (e.g. about 20 or 30
fold) had been brought about as would increase the pressure to
within the limits above stated. If, on the other hand, the initial
pressure was comparatively high (e.g. 0""-1), then a much smaller
diminution (two or three fold) of volume was required to produce
the afterglow.
19. By regulating the rate at which compression was produced
the brightness and duration of the glow could be controlled to a
certain extent. The phenomena observed in this connection were
all in conformity with the idea that in a given mixture and
quantity of gas in the pump-bulb a definite amount of energy was
to be got rid of by radiation for a given alteration of pressure, and
that the time-integral of the intensity of the pressure-glow was
approximately constant.
20. Attempts were made to obtain the pressure-glow without
any electrical excitation like that described in § 16. The appa-
ratus was left in complete working order one evening, and the
next morning (i.e. after an interval of 15 or 16 hours), the rarified
gas was compressed, but there was no glow:—that is to say, the
energy requisite for the formation of the low-pressure-compound
had not passed into the gas.
A strong beam of light was passed through the gas, in the hope
that this would communicate the requisite energy. But there
was no glow.
Electrical excitation was applied (as described in § 16), and
the pressure-glow was as bright as before.
21. The actual distance between the tube for the electrode-
less discharge and the pump-bulb was not more than 18 inches,
but the connecting tubes were about 6—7 feet long. Very few
electrodeless discharges in the tube were enough to put the gas in
the pump-bulb into the state requisite for the production of the
pressure-glow. The same gas was used again and again with
apparently no uncertainty in the phenomena exhibited.
22. In order to make the conditions more simple, I sur-
rounded the pump-bulb itself with a coil of thick wire and
attempted to produce the electrodeless discharges in the pump-
bulb: but though I have generally found it easier to produce the
1897.] the compression of certain rarified Gases. 301
discharges in large bulbs than in small tubes, I could not get the
discharge to pass. The failure was attributed to the fact that the
inner walls of the bulb were always wet with strong sulphuric
acid, some of which floated on the surface of the mercury.
23. It may be noted here that the mercury in the pump was
connected with earth through wires and the gaspipe system.
This fact constitutes a difficulty in the way of explaining the
pressure-glow as simply a phenomenon of electrical origin in which
the compression plays a secondary part.
24. The explanation of the pressure-glow appears to me
rather to be in general agreement with the explanation given by
Sutherland (Phil. Mag. 1897, Mar.) of anomalies observed by
Bohr and Crookes in the compression and rarification of oxygen.
According to Sutherland, in the rarification of oxygen a point 1s
reached (pressure 0™"-7) when oxygen begins to be converted into
ozone, and below the pressure 0™™15 the gas is entirely
ozone. Between the pressures 15™" and 0™ 7 the gas obeys
Boyle’s Law as oxygen, and below 0™"15 it obeys Boyle’s Law as
ozone. Between the pressures 0™™7 and O"™™15 the gas is a
mixture of oxygen and ozone. Sutherland is led to the view that
in the compression of ozone from the lowest pressures, the ozone
begins, when the pressure reaches the value 615, to be knocked
to pieces in virtue of the frequency of collision between ozone
molecules being the same as that of some natural vibration in the
molecule.
25. If Sutherland's views be correct in the case of ozone and
oxygen, it is probable that there must follow a generalization of
them to cases where mixtures of different gases are concerned.
[Since the subject of this note was communicated to the
Society, an abstract has appeared of a paper by Prof. Threlfall
and Miss Martin (Nature, Vol. 56, p. 288) in which an experiment
was made with the object of investigating whether oxygen can
form ozone simply by virtue of a reduction of pressure, and the
authors come to the conclusion that either no ozone is formed, or
if such formation does occur, it is to an extent less than 0°005 per
cent. of the volume of the gas employed. The nature of the
indicator is not described in the abstract referred to. ]
Spectrum of the ‘pressure-glow.’
26. The spectrum of the gas glowing during compression 1s
very marked and consists of a faint continuous spectrum with
four conspicuous bright bands coinciding with those which
Schuster has described as belonging to the spectrum of the nega-
tive glow of oxygen.
302 Mr Newall, On Luminosity attending Compression. [Apr. 26,
27. The contrast of this spectrum with that of the electrically
excited phosphorescence (§ 6, 7) is very striking. In one case of
the electrical phosphorescence the oxygen bands were seen, under
circumstances however which led me to believe that they were
really due to compression. The pressure in the tube for the
electrodeless discharge was so low that the electrically excited
phosphorescence was very faint, but whilst the phosphorescence
was still persisting, more gas was let out of the reservoir into the
pump and tube. Without any fresh electrical excitation, the phos-
phorescence increased in brilliance and the oxygen bands were
seen in the spectrum. In no other cases of electrically excited
phosphorescence have I seen any but a continuous spectrum.
It may be that the difference in the spectra in the two cases
will suggest further investigation. I am not able to offer any
explanation.
It is to be regretted that the investigation of the pressure-
glow is made so difficult by the apparent importance of what may
be described as impurities. I am not able to recover with any
certainty the mixture of gases capable of exhibiting the pressure-
glow, and can only say that oxygen with traces of nitrogen and
SO, is the mixture I should begin upon, if I wished to recover
the conditions that obtained when I made the experiments about
two years ago.
Possible bearing of the phenomena of pressure-glow on astro-
nomucal matters.
28. The origin and mechanism of the luminosity of nebule and
the persistence of their general outlines and details are subjects
that have occupied the attention of astronomers at various times ;
and the idea of necessarily elevated temperature is losing ground.
The mere fact that a rarified gas can be got into a state such
that compression causes 1t to glow and emit a band spectrum is
suggestive.
If we admit a slow condensation going on in a gravitating
mass of gas, whether it be gathered into globular form or
irregularly extended like the nebula in Orion or’ surrounding
stars like the Pleiades, then we should be led by the phenomena
of the pressure-glow described in this note to conceive of the
possible existence of a surface or layer of luminous matter, outside
which luminosity would be inappreciable because the pressure was
too low, and inside which the pressure was too high for luminosity
of the kind considered. The gradual streaming in of rarified gas
through the region when the conditions are favourable to the
production of pressure-glow would account for the maintenance of
the luminosity and the persistence of outline.
1897.] Mr Darwin, Observations on Stomata, ete. 303
Monday, 10 May, 1897,
PROFESSOR LIVEING, VICE-PRESIDENT, IN THE CHAIR.
The followmg Communications were made to the Society :—
(1) Observations on Stomata by a new method. By FRANCIS
Darwin, M.A.
16
Our knowledge of the behaviour of stomata is defective
principally for want of good methods. The earlier workers simply
stripped off the epidermis and examined the stomata microscopi-
cally. This plan is obviously untrustworthy and has been replaced
by a better method, ze. cutting surface sections. This is less
inaccurate but is still open to the objection that it does not give
evidence of the condition of the stomata in the uninjured leaf.
Where the stomata are large it is possible with a microscope to
see whether they are open or shut in the uninjured leaf; this is
the method followed by Kohl*. The chief objection to this plan
is that it can only be used in certain selected plants, e.g. Trianea,
Caltha, and that it is laborious and requires considerable practice.
Lastly, there is the method of N. Miiller+, in which the condition
of the stomata is estimated by the rate of flow through them of a
stream of air.
Another set of methods are indirect in character and depend
on the fact that in aerial leaves the loss of watery vapour takes
place almost entirely by the stomata and not by the cuticle.
In a leaf with stomata on the lower surface only, transpiration
is all but confined to that surface. Such a leaf placed between
two glass plates will bedew the lower but not the upper plate.
Various methods have been founded on this basis.
Merget{ used paper soaked in mixture of certain salts of
palladium and mercury, the paper is applied to the surface of
the leaf and becomes black or brown owing to the moisture
coming off from the stomatal side.
* Botanisches Beiblatt zur Leopoldina, 1895.
+ Pringsheim’s Jahrbiicher, Vol. v11t.
$ Comptes rendus, 1878.
304 Mr Darwin, Observations on Stomata [May 10,
In 1894 Stahl* introduced his cobalt method, in which he
took advantage of the fact that paper impregnated with cobalt
chloride is blue when dry, and becomes pink in damp air. Thus
if dry cobalt paper is placed on each surface of a hypostomatal
leaf, the paper rapidly changes to pink on the lower side, but
remains blue on the upper surface. Whereas when the stomata
are shut no such difference is seen. With this method Stahl
has made out a number of most interesting facts. It is moreover
a method especially applicable to demonstration and lecture
purposes, since the effect is rapidly obvious, and clearly visible
from a little way off.
In the Practical Physiology, 1894, of Mr Acton and myself,
I described a rough hygrometer in which the index was the
awn of Stipa, and which I used to demonstrate that transpiration
is ordinarily stomatal rather than cuticular.
The method which I have to describe is like Merget’s and
Stahl’s papers, and like my Stipa hygrometer, an indirect one,
depending on the yield of watery vapour from the stomata.
Two or three years ago I came across a toy consisting of the
figure of a man cut out of a thin sheet of horn prepared in such
a way as to be extremely hygroscopic. When placed on a damp
surface it writhes and twists, curving away from the source of
moisture. The toy had lain hidden in an old house for something
like 100 years; 1t was made for fortune-telling purposes, the
degree of movement on the hand indicating the disposition of
the patient. The material was described as Chinese sensitive
leaf; it is mentioned in Holtzappfel’s Turning and Mechanical
Manipulation, Vol. 1, p. 123, 1846, as made from pressed horn.
Similar toys in the form of fishes were described by Maria
Edgworth, 1808, and appear to have come from Japan. Figures
of women and also of fish, made apparently of gelatine or gold-
beaters’ skin, are still sold for fortune-telling. But these are not
so good for my purpose as horn sheets. Being unable to obtain
any more of my original material I made use of shavings of
horn and for a long time despaired of making them sufficiently
sensitive. At last a chance observation showed me that the
horn shavings are rendered sensitive by heat.
The method of using the material is as follows. A strip of
horn sheet 8 or 9 mm. long by 3 or 4 wide is fastened by
one end to a small block of cork so that the horn lies flat on
any surface on which the instrument is placed: the horn bears
at its free end a bristle to serve as an index. When it is placed
on a damp surface the index instantly rises to an angle of 20°
to 50° or even more, whereas it remains flat on a dry surface.
* Bot. Zeitung, 1894.
1897. ] by a New Method. 305
A paper-scale being fixed to the cork block serves to read off
the movement: when applied to leaves, for instance a hyposto-
matal leaf, the reading is zero on the upper side and varies
on the other side according to the state of the stomata. It
has been hitherto impossible to get any physical measure of
what the readings indicate; from a large experience of various
leaves it may be said that 50° means an extreme amount of
transpiration, 30° fair degree, 10° a small degree.
It is sometimes difficult to know how far the readings of the
hygroscope can be taken to indicate the state of the stomata.
Thus for instance in variegated leaves I get low readings on
the white parts, high readings on the green parts. Is this due
to partial closure of the stomata or to there being fewer stomata
on the white patches, or is it because the absence of chlorophyll
diminishes the yield of vapour? If the method fails in cases
like this it is nevertheless applicable in broader, less critical issues.
For instance, all microscopic observations from the time of Mohl
agree that certain leaves close their stomata when they wither.
It cannot be doubted therefore that the drop in the hygroscope
readings in withering leaves corresponds with closure: the same
argument applies to the effect of darkness. By taking readings
on the uninjured leaf of Caltha and by looking at the stomata I
have convinced myself that there is a rough agreement between
the hygroscopic and microscopic methods. But I generally get a
low hygroscope reading even when stomata look quite shut.
If we may believe that broad differences in hygroscope
readings represent differences in the openness of the stomata,
we must not assume that where the hygroscope stands at zero
there is absolutely no loss of vapour from the leaf. Thus there
is no doubt that leaves lose some water by cuticular transpiration,
yet the hygroscope always reads at zero on a surface free from
stomata. Alsoa leaf whose stomata are apparently shut as indicated
by the hygroscope, continues to lose weight by evaporation.
Since the movement of the index depends on the difference
between the moisture of the air on the two sides of the horn
plate it might be supposed that a given surface would give very
different readings in damp and dry air. But practically this is
not so. I used a porous brick standing in a shallow layer of
water; on the brick I placed a sheet of perforated zinc and on
this the hygroscope; readings were taken in the dry air of the
laboratory, in the less dry succulent house and in the various plant-
houses, and I got no very serious differences in the readings.
Another source of error is that the horn plate is affected by
heat, ze. it curves away from a hot surface. This makes it
difficult to experiment on the effect of heat, but otherwise is
unimportant.
306 Mr Darwin, Observations on Stomata [May 10,
It is impossible to make two instruments identical, so that
the readings of one instrument are not strictly comparable with
another. The chief use of the hygroscope, and for this it is
admirably suited, is to compare the leaves of an experimental
plant with those of a control, or to observe sudden or gradual
changes of reading on a given leaf.
Jif.
In a forthcoming paper I shall give a full account of the
results which I have obtained. In the present publication I give
a brief statement of the facts which may be easily demonstrated
with the hygroscope, together with some results which are believed
to be new.
1. The hygroscope index remains at zero on the upper surface
of a hypostomatal leaf, indicating that there is a low degree of
transpiration from that surface.
2. There is active transpiration on the lower surface of a
floating leaf (e.g. Nymphaea) when exposed to air.
3. In a terrestrial leaf with stomata on both surfaces, the
behaviour of the stomata is different on the two surfaces. Thus
the upper stomata are more sensitive to external conditions and
are frequently shut when the lower ones are opened.
4, The typical stoma closes (either wholly or partially) in
darkness. The process is not a sudden one, the readings of the
hygroscope fall gradually to zero. It is difficult to generalise as to
the time which closure in darkness or opening in light requires;
half-an-hour would represent fairly rapid effect.
5. The natural diurnal course of the stomata can be easily
followed by taking readings throughout the day and the behaviour
of the stomata thus graphically represented. The rise in the
early morning and the fall at night are both rapid, the inter-
mediate region of the curve may be either more or less flat, or it
may present a continuous rise and fall.
6. A certain degree of closure at night is almost universal in
typical terrestrial plants and is generally absent in water-plants
and marsh-plants*. Since the hygroscope does not distinguish
between partial and complete closure, these results are not neces-
sarily at variance with those of Leitgeb f.
7. The nocturnal closure is a periodic phenomenon: this is
not so strongly marked as the nyctitropic movements of leaves,
since the stomata of a leaf placed in a dark room at night are
not found to be open in the morning.
* Caltha and Trianea however close at night.
+ Mittheilungen aus dem Bot. Institut zu Graz, 1886.
1897. ] by a New Method. 307
The existence of periodicity may be best demonstrated by the
method employed by Pfeffer in observing the “sleep” of flowers,
namely, by seeing that they behave differently to a given change
of temperature at different times of day. The case is the same
for stomata. In the morning a much longer period of darkness
is required to close the stomata than is necessary at night: on
the other hand stomata which are closed, open in the light much
more easily in the morning than in the late afternoon.
8. The well-known result that the stomata close when a leaf
is cut from the plant and allowed to wither is strikingly
demonstrable with the hygroscope, the readings sinking gradually
to zero.
In this way the fact observed by Stahl can be confirmed,
namely, that the leaves of marsh and water-plants do not, as a
rule, close their stomata on withering.
The closure of the stomata produced by watering plants with
dilute NaCl solution has also been confirmed *.
9. In some cases the process of withering is strikingly
different. In Pointsettia, Tropaeolum, Campanula vidalit and
some other plants the closure of the stomata is preceded by
well-marked opening—as the following figures will show.
hr min _ hygroscope
4.10 =10
12 =10
12:2 leaf cut off
13 =18
14 =15
15. -=22
18, )=20
23.5 | = 15
25 =10
I 12
5a) 0
The result is of some importance as bearing on the question of
mechanism.
The effect of cutting off the water supply must be to
diminish turgescence—and diminished turgescence of the guard
cells must mean closure. Therefore the opening of the stomata
must be due to the loss of turgor in the other elements of the leaf,
especially of the ordinary epidermic cells—the final closure
being due to the withering of the guard cells+. This effect is
especially well seen in plants with milky juices, eg. Campanula
* See Schimper, Indo-Malayische Strand Flora, 1891.
+ On this subject see Leitgeb, loc, cit,
308 Mr Bateson, Notes on Hybrid Cinerarias. [May 10,
vidaliz, Pointsettia. I imagine that the laticiferous vessels supply, .
as it were, an efficient system of drainage by which a large
quantity of fluid can at once escape, and therefore quickly alter
the internal pressure in the tissues.
My work also bears on the question of mechanism in another
way. It has been assumed, I believe, incorrectly, that light opens
the stomata because the assimilation of the guard cells leads to
osmotic material being built up; the closure in darkness being
due to loss of such osmotic matter.
Schellenberg* has sought to uphold this view by placing
leaves in air free from CO,, where he finds that the stomata
are shut. In none of my experiments did I see any signs of
closure being due to absence of CO,.
But in any case, another of my results is unfavourable to
this view. Many plants reopen their stomata if they are kept
continuously in the dark for several days. Whatever is the
explanation of this fact it is clearly not due to returgescence of
the guard cells owing to assimilation. This fact was first observed
by my assistant, Mr Elborn, to whom I am indebted for much
valuable help.
(2) Notes on hybrid Cinerarias produced by Mr Lynch and
Miss Pertz. By W. Bateson, M.A., St John’s College.
It is stated by many writers that the garden Cineraria arose
as the hybrid offsprmg of several species of Senecio from the
Canary Islands. This statement has been questioned by Mr
Thiselton Dyer on various grounds. The author exhibited
hybrids raised from S. cruentus, S. multiflorus and S. Heritieri
(= lanatus) raised in the Cambridge Botanic Gardens by Mr Lynch
and Miss Pertz which illustrated the great variability which
appears in the offspring of the various crosses. In particular,
specimens of Heritieri 2 x cruentus § and of the reciprocal cross
were produced, showing excessive variability and proving how
greatly the peculiar characters of Heritiert may be obscured in
the offspring, even of the first cross. Five specimens of multiflorus
¢ x Heritiert § were exhibited, each of which was quite distinct
from the rest. Experiments had entirely confirmed Darwin's ~
observation that Cinerarias are self-sterile in a high degree.
They hybridize on the contrary with great readiness. An acci-
dental hybrid between Heritiert 2 x garden Cineraria ¥~ and the
reciprocal were also shown, the two plants being quite unlike
each other, the former being an upright plant of a rather woody
habit, resembling poor specimens of the garden Cineraria, while
* Bot. Zeitung, 1896.
1897.] Mr MacBride, The Relationship of AMPHIOXUS, etc. 309
the reciprocal (illustrated by two specimens of independent origin)
was a struggling plant with large pale flowers having almost a
procumbent habit, differing considerably from both its parents.
One seedling multiflorus $ x garden Cineraria § had been pro-
duced which was almost entirely female, a few anthers only
appearing in later inflorescences. These experiments were to be
continued, but so far as they had gone they were entirely con-
sistent with the view that the Cineraria was a hybrid between
several species, cruentus, Heritiert and probably multiflorus being
among them. The two first are named by most authorities as
probable parents.
It was proposed to publish details of the experiments when
those of the next year should be completed.
Monday, 24 May, 1897.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
The following were elected Honorary Members of the Society :
Major Percy Alexander MacMahon, R.A.
Prof. Charles A. Young, Princeton.
Prof. Albert A. Michelson, Chicago.
Dr Ludwig Boltzmann, Vienna.
Prof. Augusto Righi, Bologna.
Prof. Dimitri Ivanowitch Mendeleeff, St Petersburg.
Sir Archibald Geikie.
Prof. Edward Salisbury Dana, New Haven, Conn.
Sir John Kirk.
H. H. Albert, Reigning Prince of Monaco.
Rev. Canon Alfred Merle Norman, Durham.
Prof. Wilhelm Pfeffer, Leipzig.
The following Communications were made to the Society :
(1) The relationship of Amphioxus and Balanoglossus. By
EK. W. MacBripg, M.A., St John’s College.
In seeking for some light as to the origin of the great
Vertebrate phylum, the only safe course is to examine with great
care the anatomy and development of the least differentiated
forms known to us which show traces of Vertebrate structure.
310 Mr MacBride, The Relationship of [May 24,
The simplest animal which is universally recognised as a
Vertebrate is Amphioxus, and the study of its anatomy and
development has thrown a flood of light on the meaning and
origin of many of the organs in the higher Vertebrates. If
however we desire to trace the Vertebrates further back than
Amphioxus, we find no consensus of opinion as to the direction
in which we should prosecute our search. Dohrn supposes that
we ought to go in the direction of the marine Annelid worms.
This Society has recently had presented to it by a distinguished
fellow, an elaborate paper, pleading for the affinity of Vertebrates
with the Arthropoda; whilst, as we all know, Bateson’s view,
that Balanoglossus is the lowest animal with traces of Vertebrate
structure, has been widely accepted here, though it has not met with
the same favour in Germany.
It must be admitted that Balanoglossus is about as unlike
a Vertebrate externally as one can well conceive, and it is difficult
to imagine that the dominant Vertebrates should have taken their
origin from a mud-inhabiting worm. One of the most prominent
features in the organization of the lower Vertebrates is the
division of their muscles into segments, a feature which they
share with the Annelids, and to which it is hardly possible to
compare the division of the body of Balanoglossus in three regions
—head, collar and trunk. The main object of this essay is to
show that there exists in the Amphioxus larva an analogous
division of the body which precedes in order of development the.
segmentation of the muscles.
In a former paper on this subject, I showed that the ccelom
in Amphioxus originated at three distinct points from the
alimentary tube.
(1) At the dorsal lateral corners a pair of hollow ridges
become constricted off from the rest of the gut, and then by
the obliteration of their lumen at various points, divided into a
series of distinct sacs. These processes go on progressively as
the animal grows in length—the ridges continuing to com-
municate with the gut behind, long after they have been
completely separated from it and divided into segments in
front.
(2) A pair of pouches grows out of the gut in front of the
foregoing and nearer the mid-dorsal line, these give rise to the
first pair of muscular segments and to other structures as well.
(3) The most anterior portion of the alimentary canal becomes
separated off from the rest, and becomes immediately divided into
a pair of cavities of which the right becomes large and thin-walled,
whereas the left becomes a small thick-walled sac which acquires
an opening to the exterior.
1897.] AMPHIOXUS and BALANOGLOSSUS. 311
Now these sacs practically give rise to all that is contained
between the skin and gut of Amphioxus with the exception of
the notochord and the nervous tube. In the paper referred to
I compared (3) to the head ccelom of Balanoglossus, and
(2) and (1) to the collar and trunk ccloms respectively of that
animal.
It is & priori improbable that any form exactly like the
ancestor of a living animal has survived to this day. For ew
hypothest such a type of structure has been found to be unsuited
to the environment and has been modified by the struggle for
existence. If, however, whilst some of the ancestors of Vertebrates
were undergoing evolution into higher forms under the stress of
competition, others betook themselves to situations, like the
mud, where they could escape the brunt of the struggle, such
animals would preserve the general level of ancestral structure
in a more or less degenerate form with special adaptations to a
burrowing life, and this we suppose Balanoglossus to have done.
In the higher Vertebrates the homologue of the head cavity
has been detected in that bilobed head cavity which in the
embryos of fish underlies the eyes, and from whose walls the
majority of the eye muscles are formed, but the homologue of
the collar cavity has not yet been sought for and naturally has not
yet been discovered.
In my former communication on this subject I alluded toa
paper by Lwoff on the development of the germinal layers in
Amphioxus. In this paper Lwoff not only maintains that the
celom or body cavity does not originate from the alimentary
canal, but that the whole mesoderm and the notochord itself
originate from an ingrowth of the ectoderm. If this were true
any possible comparison of Balanoglossus and Amphioxus would
be rendered impossible; it would be a result of the most far-
reaching character. It may be remarked that it used formerly
in many cases to be asserted that the ectoderm gave rise to the
mesoderm where later renewed research has shown that the
mesoderm arose from the alimentary tube.
I have now further evidence to offer in favour of this view.
As I have said, the trunk ccelom becomes divided into separate
muscular segments, these later become differentiated into a dorsal
muscular and a ventral thin-walled portion; and then the dorsal
portions become completely separated from the ventral parts,
and simultaneously the latter become fused with one another to
form two longitudinal coelomic canals.
What I have designated as the collar coelom undergoes also
differentiation into a dorsal muscular and a ventral thin-walled
portion. The two do not however for a long time become con-
stricted off from one another; and even when this occurs the
VO, EX. PT. VI, 25
312 Mr MacBride, The Relationship of [May 24,
ventral part does not become confluent with the ventral part of
the trunk celom. The ventral part of the collar ccelom grows
back externally to the trunk ccelom, forming two ventral lateral
ridges which reach some little distance behind the last gill-slit
which is formed. These ridges, which are traceable as soon as
the mouth and first gill-slit have been formed, are really the
first rudiments of the atrial folds, which later hang down over
and cover the gill-slits. The ccelom contained in these ridges
gives rise to the ventral muscle of the atrial cavity. Now in
Balanoglossus the hinder end of the collar extends over and covers
the first gill-slit, and the suggestion of Bateson that this re-
presents the first beginning of the formation of an atrium like
that of Amphioxus is borne out by the facts I have just narrated.
I have said above that it was difficult to suppose that active
Vertebrates were descended from a sluggish worm like Balano-
glossus. It is however unnecessary to make such a supposition:
when zoologists point to one existing animal as “representing”
the ancestor of another, they often use loose and inaccurate
language.
The evidence that Lwoff brings forward in support of his
position is exceedingly feeble. The first shape which the de-
veloping egg of Amphioxus assumes is that of a hollow sphere—
the so-called blastula: this then becomes converted into the
well-known gastrula by the process of invagination, one half being
pushed inside the other. Now Lwoff maintains that in the
blastula certain cells are distinguished from the rest by their
size, and that these alone represent the endoderm of other
animals, they are first invaginated, and then the invagination of
cells which are really ectoderm succeeds to this. Considering
that the invagination is a continuous process which proceeds
regularly to its completion, and that when it is completed no
difference in the character of the invaginated cells can be detected,
it will be seen that this is a most violent and arbitrary interpre-
tation of the facts, which could only be entertained if it were
shown that in the blastula the endoderm was clearly and sharply
defined. I have cut about a hundred of invaginating blastule to
examine this point and can meet it with a direct denial.
It is true there are certain cells of the blastula distinguished
by their larger size from the rest, but these merge gradually into
the rest at the sides, and where the process of invagination just
shows itself the smallest cells are found. This shows that the
size of a cell depends on the rapidity with which division is going
on, and as the process of invagination is connected and in fact
caused by division and multiplication, it is natural that smaller
cells should be found at the edges of the area which is about to be
invaginated,
1897.] AMPHIOXUS and BALANOGLOSSUS. 313
As a matter of fact, although these small cells just appear
at the spot which will become the dorsal lip of the blastopore,
where Lwoff imagines the ectodermal invagination which is to
give rise to the notochord to take place, it 1s the other lip which
in the later stages exhibits it most clearly.
It is true that in those higher Vertebrates in which the process
of invagination can be clearly traced, the cells composing the upper
wall of the primitive alimentary tube are small compared to those
forming the under part of the wall, these being choked with yolk;
and great stress is laid by Lwoff on this fact. The obvious and
simple explanation is, that the processes of folding, which the
dorsal wall has to undergo in order to give rise to the notochord
and the mesoderm, would be rendered impossible were the cells
composing it to be overcharged with yolk, and hence the yolk
is confined to the cells forming the ventral wall of the gut.
(2) On the degree of the Eliminant of Two Algebraic Equations.
By R. Lacutan, Sc.D., Trinity College.
The object of this paper is to show how the degree of the
eliminant of two algebraical equations may be determined in a
very simple manner by geometrical considerations. So far as I
am aware the only method given in the ordinary text-books is
that given by Serret,—Cours d’ Algébre supérieure, 4th edit. vol. 1,
§§ 278—280, which method is due to Minding. Although not
difficult to apply to particular cases, it does not seem to be so
simple as that here given.
1. Consider two curves C,,, C, whose equations expressed in
homogeneous coordinates are
Fm (&, Yy, z)=0,
Falt. y,2)=9%.
If z be eliminated from these two equations we obtain an equation
of degree mn, say
Pian (x, y) = 0,
which represents the lines connecting the point «=0, y=0 to
the mn points of intersection of the curves Cy, Cn.
Now of these mn points some will usually be found on the
lines a, y, z forming the triangle of reference, and some will
314 Dr Lachlan, On the degree of the [May 24,
usually be coincident with the vertices of the triangle. Excluding
all these points let us suppose that there are r points of inter-
section which do not lie on the lines a, y, z; and let ¢,(#, y)=0
be the equation which represents the line connecting these points
to the point «=0, y=0.
Then ¢,(#, y)=0 is what is usually called the z-eliminant of
the equations
Tin (® Y, 2)=9, fa(%s Y, 2) = 0.
2. It is obvious from this method of forming the eliminant
of two equations, that, whichever one of the three variables be
eliminated from two homogeneous equations, the result is of the
same degree.
This fact may often be used with advantage.
As an example, suppose we require the degree of the eliminant
when 2 is eliminated from two equations of the form
Um + Uy = 0,
Un + dug = 0,
where Um, Up, Un, Wq denote functions of #, y of degrees m, p, n, q.
Here if X be eliminated the eliminant is
UmUg — Untlp = 0,
and is of degree equal to the greater of the two numbers m+q
or N+ Pp.
Hence, if w be eliminated from the two equations the eliminant
will contain > in the degree m+q or n+p, whichever is the
greater.
Similarly, it follows that the discriminant of
Um + Mp = 0,
will contain » in the degree m+p—1.
3. The degree of the eliminant of any two equations is to be
found by arranging the equations in a homogeneous form, intro-
ducing if necessary other variables. The equations are then to
be considered as representing curves, and the number of points
of intersection which lie on the lines forming the triangle of
reference has to be determined. The degree of the eliminant is
equal to the product of the orders of the curves diminished by
the number just determined.
1897.] Eliminant of Two Algebraic Equations. 315
To illustrate the method let us take the example given by
Serret. He takes the equations
(a, 2) y' + (@, 2)y + (@, 4) y+ (@, 5)y + (#, 5)=0,
(x, 8) y° + (a, 6) y+ (@, Ny +(@, 4) y¥* + (@, 3)y + (@, 4) = 0,
where (a, 7) denotes an integral expression of the rth degree in «.
Introducing z, so as to make these equations homogeneous, we
have the equations of two curves, C,, C3;
(a, 2). yi + (a, Z)2 y°2 + (&, 2) y+ (&, Z)sy + (a, 2)52 = 0,
(a, Z)3 y° + (a, Z)g YZ + (2, Z)y YZ + (2, 2), Y72" + (H, Z)s Yo? + (a, 2),2°=0,
where (a, 2), denotes a homogeneous expression of the rth degree.
The only common points of the curves C,, Ci; which lie on the
lines #, y, 2 coincide with the points s=z=0, and y=z=0.
In fact, at the point e=z=0,
C, has two branches, given by equating the coefficient of y* to
zero,
C,, has eight branches, given by equating the coefficient of y°
to zero.
Hence at this point there are 2 x : points of intersection of
the curves.
Again, at the point y= z=0,
C, has one branch, given by equating the coefficient of * to
zero,
C; has two branches of the form
y +arz=0 and y*a* + 628 =0.
Hence at this point there are 4 points of intersection of the
curves.
Hence the order of the eliminant of the equations
=6x13—2x8-—4=58,
which agrees with Serret’s result.
4. The following examples are of some importance.
Ezx.1. If @ be eliminated from the equations
Di We ip
+0" by + me ee Gn +0
An, he Af, Lean An En
+0 a,+é@ On +6
the degree of the eliminant is n—1.
=1,
= 1,
316 Dr Lachlan, On the degree of the [May 24,
Introducing &, 7 to make the equations homogeneous, we may
write them in the form
EX; is Ea, + ELn,
= Jes —l=
ayn + 0 ‘mee Ann +O Q
A, &a A, £4; A, €a
C= 1¢%1 2X2 pak eee OSPR Oe
ant an +6 aan +6 ie
C and ©’ are curves of the nth degree, having » common points
on the line €=0, viz.
ant+O0=0, an+0=0, &e.,
and (n—1) branches passing through the point »=0=0, and no
branch of one curve touches a branch of the other.
Hence the order of the eliminant is
v—n—-(n—-1P=n-1.
This result may also be inferred from § 2, for if & be
eliminated, the result is obviously of degree (n—1) with respect
to » and @.
Ex. 2. The discriminant with respect to @ of the equation
Ly L2 Ln
G+0' tO Uo vance
is of the degree 2 (n — 1).
We have to find the degree of the eliminant of
=i,
Ex, Ex, i Ey st
GaGa ad eaenen mm
v x. Ln
ue ee Uk ae Oe
(an+ Of (an+0 "+ G@m+oy
while the latter equation represents 2(m—1) lines through the
point »=@=0, the degree of the eliminant must be 2 (n—1)
(§ 2).
Ex, 3. If @ be eliminated from the equations
nn a oe § el
GOR Gree) Gees a
Aja, Ass A pln,
GeO Gaon 1 GE Oe ;
the degree of the eliminant is np — q (p > q).
1897.] Eliminant of Two Algebraic Equations. 317
This is obvious by eliminating & from
Ea, oe. Extn ie
(ayn a oye eee (Qn +0)? ‘oles
A,a€ Anan at
(an + 02 oe (Ann +6)2 ae
Ex, 4, If 0 be eliminated from the equations
av x
1 V n vs
(q+ 0% * @+opt t@ top”
Ayr, Ao Paes rail
(a,+0)2! (ag 020 1 Can tO”
the eliminant is of degree (n—1)p—q(p > q).
Introducing & and 7 to make the equations homogeneous, we
may write them in the form
Ex, NX, NX
Pe a he ae a ee = en ()
(aan + 8)? * (cam + BYP (ann + 8)?
A, Ea, Ana, Anni
(aan + 8)2* (ay £0)2 °° * Cay + 8
If now we eliminate & we get
1 A, a a Aen
(an + 0)? (aan + 0)2 (tan + 02
1 Lo Zn
Garren tort terres"
If p >q, this result is of the (n —1) p—q degree with respect
to » and @.
Hence by § 2 the result of eliminating @ from the equations
will be of degree (n —1) p —q with respect to & and ».
Ex, 5. If « be eliminated from the equations
Gyo + oO + +O, Ot. +a =,
bya +... + bp ew + bet +... +b, =0;
where a,, a,, b,, b,’ contain y in the rth degree, the eliminant is
of degree 2mn.
Consider the curves
Com = Ug oe Up bt yp are +, +g 2 = 0,
Can = Vyt™ +... Up A tate 4+ te =0;
where w,, uy, Vp, Vy are homogeneous with respect to z and y of
degree r,
318 Dr Lachlan, On Algebraic Equations. [May 24,
These two curves have the point x=z=0 as a multiple point.
In fact Cy, has m branches of the form z?+ kay =0 at this point,
and C,, has n branches of a similar form.
Hence the pomt #=0, z=0 counts for 2mn points of inter-
section of the curves.
Hence the degree of the eliminant
= 2m x 2n —2mn = 2mn.
Ex. 6. The discriminant with respect to # of the equation
Qyt™™ +o. ty BOO +. + Oy B+... + ay =,
where a,, a, contain y in the rth degree, is of degree 27? with
respect to y.
The discriminant is the same as the eliminant of the
equations
Qnayv" +...+(2n-—7) a0" 71+... 4 7ra,a' +... +a, =9,
a0" +... trae +... + (2n — 1) aa" +... + 2na) =0.
Consider then the curves
Cy = 2nmyev"1 +... + (Qn — 1) UI +...
+ TU, ag +. tu, 241 = 0,
Con = UO EU OO os
+(2n— 1) ua" 2"—* +... + 2nu2"=0;
where wu,, u, are homogeneous with respect to y and z of
degree 1.
The only common points of C,,_, and Cy, which lie on the lines
x, y, 2 coimcide with «=0, z=0.
Cy has n—1 branches of the form 2+kxzy=0 passing
through z=0, z=0; and C,, has n similar branches passing
through the point.
Hence the point x=0, z=0 counts for 2n(n—1) points of
intersection of the curves.
Hence the degree of the eliminant
= 2n x (2n — 1) — 2n (n — 1) = 2’
(3) Tides on the Equilibrium Theory. By C. CHREE, Sc.D.,
King’s College. [Published in Transactions, Vol. XVI. Part 11.]
1897.] Mr Henry, Experiments on Ultra-violet Light, etc. 319
(4) Haperiments on the Effect of Ultra-violet Light on the
Conductivity of Iodine Vapour. By J. Henry, Trinity College,
Cambridge (1851 Exhibition Science Scholar, Queen’s College,
Galway).
It is well known that ultra-violet light causes negatively
charged bodies on which it falls to lose their charges, but it has
not been tried so far as I am aware whether ultra-violet light, like
Roéntgen rays, enables a gas through which it passes to conduct
electricity ; the following paper is an account of some experiments
made to test this point, the gases used being the vapours of Iodine
and Amyl Nitrite.
These vapours were used because it seemed probable that they
would show this effect of light very readily if it existed, since they
are sensitive to ultra-violet light in other ways*.
The apparatus used in the experiments on iodine vapour con-
sisted of an insulated copper disc, connected to a pair of quadrants
of an electrometer and supported on a stiff copper wire inside a
glass tube, which was closed at one end by a quartz plate, the
other end being open. This tube was fixed in a sand bath so that
it could be heated to a high temperature, the closed end being at
the temperature of the bath ; the diameter of the tube was 3°8 cms.,
and the length about 20cms. The light was given by a carbon are
and brought in a converging beam on the copper disc by a quartz
lens (see fig. 1).
to electrometer
Ere. 1.
a is a sand bath.
b, a screen to protect insulated wire from hot gases.
c, a brass cap holding quartz plate.
d, a screen to cut off the scattered light,
The copper disc had to be supported on a wire insulated out-
side the tube at e, as the iodine always destroyed the insulation of
any support inside, apparently by condensing on the insulating
substance (discs of mica), even when its temperature was as high
* Contributions to Molecular Physics, Memoir X. Tyndall.
VOL) Ex. PT: VI 26
320 Mr Henry, Experiments on Effect of Ultra-violet [May 24,
as 210° C., which was the temperature inside the tube during the
experiments. The iodine was introduced at any time when re-
quired in the end of a small glass tube and soon surrounded the
dise with vapour, which gradually escaped at the open end of the
large tube, but allowed sufficient time,—three or four minutes—
for the necessary observations.
Although a positively charged body is not discharged directly
by ultra-violet light, yet I found that the disc, although positively
charged, was discharged by the are-light when the disc was in the
tube as shown above, and also that the rate of discharge depended
on the distance “a” between the disc and quartz plate.
Table I. gives the results of some experiments on this dis-
charge, which show that it is due to the discharge of the negative
electricity induced on the quartz plate by the positive charge on
the disc, this mduced charge becoming very small as “#” in-
creases.
Column I. gives the distance “a” in cms.
, IL. gives the leak per minute in scale divisions for the
positive charge.
, Il. gives the leak per minute in scale divisions for
the negative charge.
, LV. gives the total charge in scale divisions.
Table I.
If; II. III. IV.
0:1 cm. 35 76 110
i Bice, 9°5 76 110
Ds, A fe |) 120
x 3 7 | 10
In trying the effect of the arc-light on the conducting pro-
perties of iodine vapour it was necessary to have the distance
“a” small, otherwise all the effective light would have been
absorbed by the vapour before reaching the disc, as was shown
by experiments on the leak of the negative charge with iodine
vapour present, so that it was not possible to get rid of the
positive leak by increasing the distance of the disc from the end
of the tube.
1897.] Light on the Conductiwity of Iodine Vapour. 321
Table II. gives the rates of discharge of the disc for different
values of the distance “«,” the smallest being ‘1 cm. in experiment
4; the potential of the charged disc was in each case 12 volts.
Column I. gives the sign of the charge on the disc.
, IL gives the total charge on the disc in scale divisions.
» III. gives the leak per minute due to light when there
1s no 1odine present.
, IV. gives the leak per minute due to light when there
is 1odine present.
By placing a plate of clear glass in the path of the light the
leak whether of the positive or of the negative-charge was at once
destroyed.
We see by these figures that the leak when iodine vapour is
present is always much less than when it is absent, and also, as
was to be expected, that the negative leak diminished more rapidly
with the increase of the distance “2” when the vapour was present
than the positive leak did, since in the latter case the light fell
on the quartz plate before being sifted of its ultra-violet rays by
the vapour; the diminution of the positive leak when the iodine
is present seems to show that the vapour not only does not
conduct, but even tends to prevent the escape of the negative
Table II.
|
all lf ike IV.
SHOVEO| | 50}
£ }ogdvel! 58 a} eps d
Baan 5 | 2
fe Meee.” | Gl af ve
ieee 19 | 6
Mas. P60. | of | Exp. 3
meas) 27 | 15)
Siesie ines. | a0p ee
|
electricity from the quartz plate, this effect may however be due
to the absorption in the iodine vapour of the light reflected from
the copper disc, back again to the quartz plate, this light in the
absence of iodine increasing the discharge from the quartz.
Owing to the leak of the positive charge, whether iodine
322 Mr Henry, Experiments on Ultra-violet Light, etc. [May 24.
vapour is present or not, these experiments do not prove that
there is absolutely no conduction of the charge through the
vapour due to the light on it, but they do prove that if this
conduction exists at all, it must be very small.
In testing amyl nitrite, the vapour was allowed to rise round
an insulated copper disc connected to an electrometer as before, -
Fie. 2.
but when the disc was charged positively, the arc-light caused no
discharge whatever, whether the vapour was present or not.
In another experiment on amyl nitrite, a beaker containing
some of the liquid was placed in coil “a” (fig. 2), and a bulb for
giving the electrodeless discharge in coil “b” which was in series
with “a,” and the number of turns in the coils adjusted, until a
substance of very small conductivity placed in “a” destroyed the
discharge in “ b.”
This arrangement showed the conductivity produced by the
Réntgen rays in the air in coil “a,” yet it gave no indication of
conductivity in the vapour of amyl nitrite, when the light from
an electric arc placed over the open beaker fell on the vapour.
In conclusion, I have to thank Professor J. J. Thomson for
his many valuable suggestions in the course of these experiments.
PROCEEDINGS
OF THE
Cambridge Philosophical Society.
ANNUAL GENERAL MEETING.
Monday, 25 October, 1897.
Mr F. DARWIN, PRESIDENT, IN THE CHAIR.
The following officers and new members of Council were
elected :—
President :
Mr F. Darwin.
Vice-Presidents :
Prof. Newton, Prof. J. J. Thomson, Mr Larmor.
Treasurer :
Mr Glazebrook.
Secretaries :
Mr Newall, Mr Bateson, Mr Baker.
New Members of Council:
Mr Harker, Mr Hutchinson, Prof. Liveing, Mr Skinner.
The names of the Benefactors were read.
The following Communications were made to the Society:—
VOL, IX. PT, VII. 27
324 Mr Pocklington, Electrical Oscillations in Wires. [Oct. 25,
(1) Electrical Oscillations in Wires. By Mr H. C. Pock1ine-
TON, St John’s College.
1. In this paper are discussed some problems relating to
the propagation of electrical oscillations along wires. The wire is
always supposed to be a perfect conductor, and to have a circular
cross-section, the diameter of which is small compared with the
other dimensions of the ees We have therefore to solve the
equations V?(P, Q, R)= yas P, Q, RB), conv. (P, Q, R)=0, with
q dt?
the further condition that at the surface of the wire the vector
(P, Q, &) is perpendicular to the surface. The method of solution
used is to start with the simplest solution of the general equations
and by adding an infinite number of such solutions together to
obtain one of sufficient generality. The arbitrary function which
represents the infinite number of arbitrary constants introduced
into this last solution is then found from an equation deduced
from the surface condition. This last part of the work is con-
ducted by means of approximations.
2. The simplest solution of the general equations, that
corresponding to the solution ¢=1/r of the equation V’p=0, is
given by the formulae*
Pil Qe Ail ape
~ dadz’ dydz’ — diz®
in which 27r/p is the period of the disturbance, and 27r/a(= 27V/p)
the wave-length corresponding in free ether to this period. This
result can be expressed in words as follows. The electric force
due to an elementary Hertzian oscillation with the element of
length ds as axis, is compounded of two forces; the first of these
+o7Il, where Il =e'e?*/r,
a , and the second is a
force o?II parallel to ds. This system of forces satisfies the equa-
tions of propagation of electric force everywhere excepting at the
element ds. If we place an infinite number of such elements
consecutively so as to form a curve, of which ds will then be an
elementary arc, and attribute varying strengths X to them, we
shall obtain a system of forces which satisfies the equations of
propagation everywhere except on the curve. The resulting
system of forces is
Gh Gh a a sie
CEO) = ay ) Jas Fe +o [as (U, m, n) NII.
“ Hertz, Wied. Ann. 1889, vol. 36, p. 4; Electrical Waves (tr. Jones), p. 140.
is derived from a potential function —
1897.] Mr Pocklington, Electrical Oscillations in Wires. 325
If the curve is either closed or has its extremities at infinity, this
is equivalent to
Ch 0 5 i NA OLN,
0, hy) = (+ dy’ a) | ae +a? fas(l m, ”) AII...(1).
This is a general solution containing an arbitrary function 2.
3. It now remains to consider the equation derived from the
surface conditions. At a point at a small distance ¢ from the
curve we have, neglecting all terms that are not large,
dn dn
fast 7 2 Ae loge. e?%,
and similarly for fds/XII, etc., so that, to this order of approxima-
tion,
d dn
_- — metry jenees bi oaks 2 upt
= 1255 ae Be 2uTh Log el
and similarly for Q and R.
The component of force along the wire therefore is, to this
order,
ie ee
—2|—— loge. e?*.
2 | ia +a) oge.é
The force tangential to the cross-section of the wire =0 to
this order. Hence the system of forces given by (1) is a solution
of the problem (to this order) provided that
ax
ds?
and the disturbance is propagated along the wire with velocity V
and without diminution of amplitude. This is only what might
have been expected from a knowledge of what happens in the
case of a straight wire; for if in our case we take the electrical
forces to be finite near the wire, at a finite distance they are zero.
Lon — 0) or t=.
4, It is clear that in order to obtain results of much interest
we must approximate more closely. We will now consider the
equations obtained by neglecting only small quantities of the
first and higher orders.
As given by (1) the force at any point on the wire tangential
to the axis is the same for all pomts on the same cross-section,
and contains two terms, one containing log e, the other finite.
The force tangential to the cross-section is finite and varies for
a given value of s as the cosine of some azimuth angle.
>
326 Mr Pocklington, Electrical Oscillations in Wires. [Oct. 25,
Suppose now that we shift the curve formed by the Hertzian
elements through a small distance of the second order. The
effect is to change the value of the component tangential to the
cross-section by a finite amount which varies as the cosine of
some azimuth angle, and that parallel to the axis of the wire by
an amount of the first order of small quantities.
By making such a shift of appropriate magnitude and direction
at every point, we can therefore eliminate the component tangential
to the cross-section. At the same time, the component parallel
to the wire is unaltered (to our order). Hence we may still
derive the surface condition from (1) by taking the integration
along the axis of the wire.
The condition thus obtained is
= 5 fas> — II +o? {1 fdsINII + m fdsmXII + n fdsnvIl}...(2).
5. Circular Ring. The simplest case that we can consider is
that of a circular rmg. Let the radius of the ring be a, the
radius of the wire ¢ as before, and let the axis of symmetry be
chosen as the axis of z. We shall assume X= A cos rd, where }
defines a point on the axis of the wire. This assumption will be
justified later.
At the point (a, 0, 2)
[os a =-rA |" dll sin rd
=-rA le do II, (sin cos rd + cos r@ sin r¢) e?",
0
where II, is the value that II takes when ¢ is put for (@ — d) and
0 for ¢, and is thus a function of ¢, a, z only,
= — 2rAe”! sin rd | "dT, cos Tr ;
0
2
[asian =— 4 | adglIl cos ¢ cosrd
0
Alas 0s (r+1) 6 {apt cos(r+1)¢
0
+ cos (7 — 1) 6 {apt cos (7 — 1) 6| ;
0
as above; and fdsnrX II = 0.
1897.] Mr Pocklington, Electrical Oscillations in Wires. 327
Hence (2) becomes
0= |- 2rA ress? [" dp Il, cos rd
+a°Aa cos 9 |” dp Il, {cos (r + 1) + cos (r — 14 Je ert,
or ie do Il, cos rd (1? — aa? cos ) = 0.........08. (3),
the disappearance of @ justifying the assumption made as to the
form of X. In this equation for finding a we may give to a and
z in II, any values which correspond to a point on ee surface of
the wire. The simplest values are w=a+e, z=0, and these
should therefore be chosen.
6. The special case r=1, which corresponds to the funda-
mental node of the wire, is that of the most interest and will be
investigated in detail.
In this case, (3) becomes on substituting for II, its value
(when z=0),
gana? — 2a@ cos $+ W?
il dd = {cos hb — xa°a? (1 + cos 2g)} = 0,
Va? —
Qacr cos h + ow
or, putting w=A+e,
zea? — cos 6 + F°a? cos 2
/2a (a+) (1—cos¢) +e
Quaa sin $p
Ls ik s we “ie 4
+ [a Tne (3a°a? — cos d + $a°a? cos 2h) = 0...(4),
where in the second integral ¢ has been put=0, since we are
neglecting small quantities.
The first integral in (4) is, calling 2aa=a, log "= L, and
neglecting small quantities,
1 ne IE
The second integral is, putting ¢/2 = W,
| "ay oe = : {ea (bcos A) == * cos 2y|
= Pay ee = (1+cos 4) — cos ar}
+ fay COs ee L = (1 + cos 4a) — — * cs apt (3):
328 Mr Pocklington, Electrical Oscillations in Wires. [Oct. 25,
Now, n being an integer,
2 7 see)
= | dip cos 2nrp cos (x~ sin Wr) = Jy, (2),
0
D2 sin (# sinvp) i
= JOR OU ee Nee Pay Ete
= [ day cos 2ny Shel ; diz I(x)
SLOVENIA RU ae: | adie)
0
Therefore the first integral in (5) is
CU. (Le iA ous a , at ssi ;
eg e+ (2 ") J(o)+(4 1)[ deS()} ;
and (4) becomes, on re-arrangement and multiplication by a,
be Gin ltr x J
(z 2 1) i ats eh)
3
+(2- *) J,(v)+(% 1) {. de JAo)}
a eC | ay ee ae =e (1 — 2 cos 2ap + cos 4h)
Oe 2, cos(#sin wv) — 1
+(¢-1) i, ty on 2} nO.
This equation gives # and thence a with an error of the order
of e/a. It can only be solved by trial. If however e¢ is so small
that errors of the order of 1/Z? can be neglected, we may use an
approximate solution of the above. A first approximation is 2 = 4
or «=2. A second is obtained by putting 2=2 on the right-
hand side of (6). This gives
(F x 1) L =485 — 70381,
so that
a= = (1 +(-243 — 3510)/D}.
Hence the period of the oscillation is equal to the time re-
quired for a free wave to traverse a distance equal to the circum-
ference of the circle multiplied by 1 —-243/Z, and the ratio of the
amplitudes of consecutive vibrations is 1 : e?*”¥ or 1 : 1—2°21/L.
It is easy to verify from first principles that the decrease in
amplitude of the vibrations is of this order,
1897.] Mr Pocklington, Electrical Oscillations in Wires. 329
7. Induced Vibrations in a Ring. We will now consider the
case of a ring upon which plane waves are incident in a direction
parallel to the axis of the ring.
Let the coordinate axes be chosen as before, and let the
incident vibration be given by
Pi Oe eee
The tangential force at the point @ due to this wave together
with a disturbance induced in the wire of the fundamental mode
and magnitude B, is to be equated to zero, giving
7 hts
0 = Ae?* cos 0 — 2 Be? — | d¢ II, cos p (1 — a7a? cos dh).
0
If we neglect e/a in comparison with unity, this becomes, as in § 6,
2B Ee bbe )
0=A4+— |2-5+(¢-1) Li
ur a Fie QZ %
i |- = Js(a)+ (2 ma =) DEQ (7 2 1) i dad, @}
a (2, cos(asin w)—1
+5] ay ae (1 — 2 cos 2 + cos 4p)
+ ([- 1) fray ae cos 24,
Unless #= 2, this gives
so that in general the induced vibration is small, and the
thinner the wire the smaller the induced vibration. The phase is
the same as or opposite to that of the electric displacement in
the plane of the ring due to the incident wave. If, however,
e=2=2+4 & where & is small, we may put # =2 in all the terms
not involving L, and get
Aad
ae 2LE +970 —1:055.°
The maximum amplitude of the imduced vibration is obtained
when 2L£ = ‘970, or a= 2/2a= {1+ °243/L}/a, i.e. when the period
of the incident wave is the same as the free period of the ring;
the amplitude then is ‘948Aa?, and the phase is in quadrature
330 Mr Pocklington, Electrical Oscillations in Wires. (Oct. 25,
with that of the wave. It is noteworthy that the amplitude of
the induced vibration is independent of the thickness of the
wire. If the incident wave is not proceeding in a direction —
perpendicular to the ring, the problem can still be solved by a
method similar to the above. The vibrations induced in the
ring will however not be confined to the fundamental, but will
include vibrations of all modes.
8. Helix. We will now consider the case of vibrations pro-
pagated along an infinite wire wound into a uniform helix. Let
the equations of the axis of the wire be e=acos ¢, y=asin 9,
z=adtanw. We shall assume X= de**, This assumption is
justified later. The value of the force tangential to the wire at
the point (a, 6, Z) is e'** times that at the pomt (a, 0, z—aé tan @).
Hence (2) gives
0= Ae! (as) ete | dpiBe'®? ll, + a? {eos wo | ddacos pe? II,
6=0 —2 -—2 hia sc
+ sin | doa tan we'®? u1 | 5
where II, is the value that II takes when ¢=0 and ¢ is put for
p— 8.
Hence 0 = de®? (aa? tan?w — B?+ aa? cos ) II)...(7).
In obtaining this equation small quantities only have been neg-
lected. If however e/a is very small, we may in this equation
neglect all finite quantities in comparison with those of the order of
loge/a. In this case we may with advantage find an approximate
value of the right-hand side of (7).
Assuming « any finite quantity, and neglecting terms that are
finite, the right-hand side of (7) is
-K Cart tan w y
Speen ea aes en Ss 22 + 2 —s 2 242
| age eet {o?a? tan?w — 8? + aa? cos d}
aa? sec?w — B?
+{" d
-K ? 2a (a + €)(1 — cos d) + ag? tan?o + &
ag ae eraad tan w
e 2a? tan?w — 8? 22 :
+f pe Feta ao an’w — 8? + aa? cos d}
The second integral is, neglecting finite quantities,
cos
— 2 (a’a? sec?w — ?) = log e.
1897.) Mr Pocklington, Electrical Oscillations in Wires. 331
The first and last can be reduced to sums of integrals of the
2) gab
form | dd oO Phi integral* is — log y to our order, and thus
the first and last integrals give
1 22 die Aly OS Dye) Tea ;
Baan, oe tan?w — 8) log (aa? tan? w — 8?)
+ te°a? log {(1+ 8 +aa tan w) (1 —8+aa tan) (1+ 8 —aa tan w)
(1 —B—aa tan w)}],
and therefore the approximate form of (7) is
2 (aa? sec? w — £?) sin w log e = (4a? tan’ w — 8”) log (aa? tan?w — B?)
+ 30a? log (1 +8 + aa tan w)(1—8+ aa tan) (1+ 8 —aa tan o)
(1 —8 —aa tan w)}...(8).
Several cases may occur. (i) In general, if a is not small, the
only term of importance is that on the left, so that
aa? sec?w — 8? =0, or B=aaseca,
and the velocity of propagation measured along the wire is
P P_y
-aseco ===
B a.
the same result as that obtained in the case of a circle.
(i) If however a and 8 are small, the first term on the right
is also of importance. If a and 8 are so small that loge can be
neglected in comparison with log (aa? tan? w — 8°), i.e. if the pro-
duct of the wave-length of the disturbance into the radius of the
wire is very large compared with the square of the radius of the
helix, we have aa? tan*w — 6?=0, or 8 =aa tan a, and the velocity
of propagation measured along the wire is
ie, Pp
Be sec @ =~ cosecw = V cosec w,
a
so that the disturbance is propagated with a velocity V measured
along the axis of the helix,
If a and @ are small, but not so small that loge can be
neglected, ie. if the product of the wave-length into the radius
of the wire is comparable with the radius of the helix, the
velocity of propagation has an intermediate value+. It is easy
to see that a like result does not follow if we try to make
(a?a? tan?» — 6?) small without making a and 8 small.
* J. W. L. Glaisher, Phil. Trans., 1870, p. 369.
+ Hertz, Wied. Ann. 1889, vol. 36, p. 21; Electrical Waves (tr. Jones), p. 158, has
proved experimentally that this is the case.
332 Mr Pocklington, Electrical Oscillations in Wires. [Oct. 25,
(iii) If one of the factors, e.g. the last, of the term under the
second log sign be small we have, since « and @ cannot then both
be small,
2 (a?a? sec?w — 8?) sin w log e= da°a? log (1 — 8 — aa tan @).
In this case we must have 8<aaseca, so that the velocity of
propagation measured along the wire must be greater than V.
There is however no superior limit to the value that it may have.
There is an inferior limit to a. Hence for periods which are not
greater than a certain value, there are two velocities of propaga-
tion along the wire, one = V given by (1), the other, > V, given
by (ai).
No other cases arise by making a and 8 great, since we must
then recur to (7), as (8) does not then hold; and here if a and B
are great, we simply have a’a*sec’w — 6? =0, the case considered
in (1).
(2) On Circles, Spheres and Linear Complexes. By Mr J. H.
GRACE.
This paper is printed in the Transactions, Vol. xvi. Part 111.
(3) Reduction of a certain Multiple Integral. By ARTHUR
Buiack. Communicated by Professor M. J. M. Huu, M.A., Se.D.,
HARES
This paper is printed in the Transactions, Vol. Xv1. Part 11.
(4) On the Gamma Function. By Mr H. F. Baker.
The Gamma Function could be defined for real values of «
by the conditions (i) that T(1)=1, (2) that P(w#+1)=aP' (a),
(iii) that, for a fixed finite h, as # tends to + 0, the difference
IY@+h) I(s)
T(a@+h) T(@)
tends always to zero. The condition (11) was well known, being
deducible from the result
I’ («) ay gees orga at
and was of suitable character for a definition; it was desirable
however to deduce it immediately from the equation
T(@)= | oe dt ;
0
this note dealt with such a deduction.
1897.| Mr Baker, On the lines of striction of a hyperboloid. 333
On the lines of striction of a hyperboloid. By Mr H. F. BaKeEr.
It was a known fact that the lines of striction of a hyper-
boloid formed two unicursal quartic curves. The most commonly
given equation shewed that the curve was an octavic curve with
six double points; such a curve on a surface of the second order
could not be a proper octavic curve; for a cubic surface drawn
through the double points and thirteen arbitrary points of the
curve would otherwise cut the curve in 12+13=25 points. The
question considered was what are the possible forms of such
octavic curves.
(5) On the Action of Uranium rays on the Condensation of
Water Vapour. By C. T. R. Witson, M.A., of Sidney Sussex
College, Clerk Maxwell Student.
I have already (Proc. Roy. Soc., Vol. 59, p. 338, 1896; Phil.
Trans. A. 189, p. 265, 1897) described experiments upon the
effect of Rontgen rays on the condensation of water vapour. These
experiments proved that the rays, in traversing moist air, in-
troduce nuclei capable of acting as centres of condensation when
supersaturation exceeding a definite limit is brought about by
the sudden expansion of the gas. Nuclei, requiring exactly the
same degree of supersaturation to enable condensation to take
place upon them, are always present in very small numbers even
without the action of the X-rays; but these rays enormously
increase their number. To produce the degree of supersaturation
necessary to bring these nuclei into play in air originally satu-
rated, a sudden expansion is necessary such that v,/v,, the ratio
of the final to the initial volume, exceeds 1:25; corresponding
approximately to a fourfold supersaturation.
In the absence of X-rays and other disturbing influences, no
condensation is observed (after the removal of all foreign nuclei)
if v,/v, is less than 1:252. If v,/v, lies anywhere between this
and 1:37 a rainlike condensation results, the drops being few
and scattered. Beyond this second limit dense fogs appear.
The action of the X-rays is simply to increase the number
of the drops which are formed when 2v,/v, lies between these limits;
the minimum expansion required for condensation not being
sensibly altered.
The experiments described in the present paper show that
nuclei of exactly the same nature are produced in moist air under
the action of the Uranium radiation discovered by Becquerel.
The form of apparatus used is represented in the accompanying
figure.
334 Mr Wilson, On the Action of Uranium rays (Oct. 25,
The thin-walled glass bulb A, about 5 centims. in diameter,
contains the air to be exposed to the action of the rays.
The tube, at the end of which the bulb is blown, is about 2°5
centims. in diameter. It has its open end ground perpendicular
to the axis, and is wired tightly down in a vertical position against
the flat surface of an indiarubber stopper.
J
Inside this tube there slides freely an inverted thin-walled
test-tube P, with the lip removed and the open end ground
smooth and perpendicular to the axis. The test-tube serves as a
piston. Its open end is always immersed in the water which fills
the lower part of the outer tube, in the way indicated in the
figure.
: By means of the arrangement B (described on p. 268 of the
paper in the Phil. Trans. already referred to) the air-space in
1897.] on the Condensation of Water Vapour. 335
the upper part of the test-tube can suddenly be put in communi-
cation with the exhausted vessel F. This causes P to fly till
it strikes the indiarubber, thus causing a sudden expansion of
the air in A. It remains tightly pressed against the surface of
the indiarubber as long as the vacuum is maintained below it,
thus preventing the lubricating water which surrounds it from
escaping.
While the piston is in this position, the extent of the next
expansion is arranged for, by opening the screw-clip 7, and
lowering the mercury reservoir f, till the pressure in A, as
indicated by the gauge, is the desired amount below the atmo-
spheric pressure. The clip is then closed and air readmitted to
the interior of the piston P by opening the tap 7. The piston
then rises till the pressure in A only differs from the atmospheric
pressure by that required to support the weight of the piston,—a
small fraction of a millimetre of mercury and negligible in these
experiments.
If B be the barometric pressure, then the pressure of the air
before expansion is
P,=B-rn,
where 7 is the maximum vapour pressure at the temperature of
experiment. The pressure of the air after expansion, when the
temperature has risen to its former value, is
P,=P,—p,
where p is the reading of the gauge, taken before the previous
contraction, as described above.
Then the ratio of the final to the initial volume is
V, Py B-ar
y P, B-r-p
Any condensation, in the form of drops, resulting from the
expansion was made visible by the light of a luminous gas-flame,
brought to a focus inside A by means of a condensing lens.
The Uranium salt (the double sulphate of Uranium and
potassium) was contained in a thin-walled glass bulb, forming a
layer about 1 centim. in depth.
The dust-particles originally-present having been removed by
repeated expansions, observations were made of the result of a
given expansion, with the bulb containing the Uranium salt
alternately 2 or 3 millimetres above A (as in the figure) and
removed to a distance.
ile v/v, = 1-245.
Result. No drops seen either with or without the rays.
336 Mr Wilson, On the Action of Uranium rays (Oct. 25,
IT. a/v, = 1°260.
Result. A dense shower was always seen when the expansion
was made with the air in A exposed to the rays; only a few
drops appearing when the Uranium salt was removed.
III. Vo], = 1273.
Result. Slight shower without the rays, a very dense shower
under the action of the rays.
IV. w/v, = 1-286.
Result. The same as in III. The showers were not appre-
ciably denser than in IIT.
More exact measurements were now made of the minimum
expansion at which the drops first begin to appear under the
action of the rays. The experimental numbers are given in the
following table.
Pressures are all given in millimetres of mercury.
Barometer = 769,
ae — lib
7 = vapour-pressure = 13,
P,=pressure of the air before expansion
= B-7=169 — 13 =756.
Gauge Pressure after | |
reading, expansion, IPI), =|, Result
P P,=P,—p
149 607 PONS i) 00
153 603 1-254 shower
149 607 1-245 | 0
151 605 1:249 shower
Thus the minimum value of v,/v, required to bring about
condensation under the influence of Uranium rays lies between
1:245 and 1:249. This agrees very closely with the value 1-252,
found with very different apparatus for air under ordinary con-
ditions (Phil. Trans. loc. cit.).
1897.] on the condensation of Water Vapour. 337
The Uranium salt shows a strong effect on the condensation,
even when the thin glass vessel containing it is completely
wrapped in tinfoil during the experiment and for many hours
previously; showing both that this material is transparent to
the agent which influences the condensation, and that the
Uranium salt continues to be active when kept in the dark.
There can be little doubt therefore that the effects on the con-
densation are really due to the radiation studied by Becquerel.
The nuclei introduced by the action of the Uranium rays, like
those formed under the influence of the X-rays, persist for some
seconds after the radiation has been cut off; for a comparatively
dense shower can be obtained, by expansions of suitable amount,
five or ten seconds after the removal of the tube containing the
Uranium salt. If, however, an interval of one minute be allowed
to elapse after cutting off the radiation, the drops produced on
expansion are not appreciably more numerous than they would
be, were the air not exposed to the radiation at all.
The nuclei produced in moist air by Uranium rays appear,
from the experiments described above, to be identical with those
formed under the action of Réntgen rays, as well as with those
always present in very small numbers in the moist gas. They
require the air, originally saturated, to suffer sudden expansion
such that v,/v, exceeds 1:25 in order that condensation may take
place upon them; the density of the vapour at the moment when
the expansion is completed being then approximately four times
that of vapour in equilibrium over a flat surface of water at the
same temperature (v. Phil. Trans. loc. cit.).
The electrical properties of gases under the action of Réntgen
and Uranium rays point to the presence of free ions. It is natural
to identify with these the nuclei made manifest in the gas under
the same conditions by the condensation phenomena described
in this and previous papers. As early as 1887 R. v. Helmholtz
(Wied. Ann., vol. 32, p. 1) and later the same author and Richarz
(Wied. Ann., vol. 40, p. 161, 1890) accounted for the effect of
electrification and chemical action in bringing about dense con-
densation in a steam-jet by supposing free atoms or ions: to be
produced by these processes. Prof. J. J. Thomson (Phil. Mag.,
vol. 36, p. 313, 1893) has explained how we should expect free
ions, in virtue of the charge they carry, to have such an effect
in helping condensation. Richarz has more recently (Wied. Ann.,
vol. 59, p. 592, 1896) found that a steam-jet reacts also with
Roéntgen rays, and again explains the phenomenon by the hypo-
thesis of free ions.
The great advantage of expansion experiments over those
made upon steam-jets is that we are able in the former to dis-
tinguish between various kinds of nuclei, by means of the different
338 Mr Wilson, On the Action of Uraniwm rays, etc. [Oct. 25,
degrees of supersaturation necessary to make condensation take
place upon them. Whatever view may be held as to the nature
of the nuclei introduced by X-rays and Uranium rays, they are
shown in this way to be identical with one another, as well as with
those existing in very small numbers in ordinary moist, dust-
free air.
Monday, 8 November, 1897.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
The following Communications were made to the Society:—
(1) On Farmer's method of demonstrating assimilation. By
Francis Darwin, F.R.S., President of the Society.
The method here given is merely a simplification of the in- .
teresting experiment described by Farmer in the Annals of
Botany’. He there pointed out that the protoplasmic circulation
ceases in an Elodea leaf kept in the dark, in a current of hydrogen:
and that the circulation recommences if the preparation 1s illu-
minated. The cessation of the movement is due to the absorption
of the free oxygen, its reappearance to the oxygen produced by |
the assimilatory activity of the chloroplasts. Farmer’s positive
results should in any case I think outweigh Pringsheim’s? failure
to observe a revival of circulation in illuminated specimens of
Chara &c., and the results which I have obtained fully confirm
Farmer's conclusions.
My object in modifying Farmer’s method was to place an
experiment of great educational value within the reach of those
who possess no apparatus beyond a microscope. This can be done
by mounting an Llodea leaf* in water and sealing the preparation
by careful rmging it with melted “ wax-mixture.”* The prepara-
tion is then placed in the dark, and the observer waits until the
available oxygen has been absorbed and the circulation has come
to rest, which takes place in from 3 to 6 hours.
1 Vol. x. p. 284.
2 Sitzb. k. Preuss. Akad. 1887. See also Vines’ interesting discussion Annals of
Botany, Vol. 1. p. 371.
3 For reasons given below it is better to mount two or even three leaves under
a single cover-glass.
4 Resin 15 parts, vaseline 50 parts, beeswax 35 parts.
1897.] Mr Darwin, On Farmer’s method, etc. eae
It is easy to show that the cessation of circulation is due to
want of oxygen by lifting the cover-glass with a needle and adding
a drop of fresh water, when the protoplasm will begin to stream
in a few minutes. The same result can—as in Farmer’s experi-
ment—be produced by illumination. The length of the period of
illumination required to start the movement varies : in a prepara-
tion darkened for about 3 hours, in which the circulation has only
recently come to a stand-still two or three minutes’ exposure
to incandescent gas light will revive the movement in two or
three minutes. When the period of darkness has lasted over
6 hours it may require 20—30 minutes... This clearly depends
on partial inhibition! of the assimilatory powers of the chloro-
plasts. If the period of darkness is still further prolonged it is
easy to reach a condition in which it is apparently impossible
to revive the circulation ; but my experiments not being especially
directed to this point I cannot say what might be the effect of
very prolonged illumination. It is to avoid the inhibition of
assimilation that I mount several leaves under one cover-glass,
so that the dissolved oxygen may be exhausted before the chloro-
plasts fall into this condition.
The method here described seems to me likely to be of value
to teachers in putting an interesting experiment within the power
of all. And it is worth noting that Farmer’s experiment has all
the educational value of Engelmann’s bacterial method. For
it demonstrates: (1) The evolution of oxygen by green. plants in
the light. (2) The connection between movement and respira-
tion and the fact that a chlorophyllous cell makes use for purposes
of respiration of the oxygen evolved within itself. (3) It
demonstrates in a rough way (what Boussingault showed to be
true for aerial plants) that assimilation can begin in the absence
of free oxygen. (4) It also demonstrates the inhibition of the
assimilating function produced by prolonged darkness.
For this last-named purpose it must be shown by the addition
of oxygenated water that the failure to circulate does not depend
on any loss of power in the protoplasm.
The method also serves well to demonstrate the effect of light
of different wave-lengths on assimilation. As a source of light
I use incandescent gas, separated from the microscope by a glass
trough through which cold water flows. For the different lights
I use Landolt’s screen solutions? in flat-sided glass vessels. In
this way the maximum effect in the red 718—639 wy can easily
be shown. The circulation, as far as I have seen, does not begin
in green? light unless the experiment is made after not more
1 See Ewart in Journal Linn. Soc. Vol. xxxt.
2 Berichte D. Chem. Ges. 1894, Vol. 27 (3), p. 2872.
3 The light is 540—505 up, @.e. it shows a narrow strip of blue.
VOL, EX, PT, VIL 28
340 Mr Darwin, On Farmer's method, ete. [Nov. 8,
than 2 or 3 hours of darkness, 7.e. when the assimilative function
is not seriously inhibited. It should be possible to demonstrate a
second maximum in the blue!, but I am here considering the
question simply from the point of view of laboratory teaching, and
in this connection I think it best to confine the demonstration
to a comparison of red and green light.
(2) Artificial Cultures of Stereum, a Timber-destroying
Fungus. By Prof. MarsaaLL WARD.
(3) On Encephalartos Ghellincki, ‘Lem., a rare Cycad. By
A. C. SewarD, M.A., St John’s College.
The subject of this note is one of the less known species of the
African Cycadean genus Encephalartos. In 1895? I called attention
to the unusual form of the fronds of Encephalartos Ghellinckia,
Lem., and figured a small piece of a leaf from a specimen in the
British Museum herbarium. A plant in the Royal Gardens, Kew,
bearing a single frond, first attracted my attention to the species.
The large and stout fronds of such species as Mncephalartos
horridus, Lehm., E. Caffer, Mig., HX. Lehmanni, Lehm., £. Alten-
steinit, Lehm., and others with broad and occasionally spinous
pinnae represent the type of plant which is usually regarded as
characteristic of the genus. Encephalartos cycadzfolius*?, Lehm.
(= E. Frederici-Gualtelmt) forms a connecting link between species
with narrower pinnae and H. Ghellinckw.
The first account of H. Ghellincku was published by Lemaire‘
in 1867, the description being founded on a plant in the nurseries
of Verschaffelt, by whom the Cycad was obtained from the central
region of South Africa. The following is Lemaire’s diagnosis of
the species :—
“Caudex ut in praecedente (2.e. Hncephalartos villosus, Lem.).
Frondes 5—12 erectae et illae ut praecedentis dispositae, totae
gossypinae metrales et ultra (quas vidi solum in prima aetate
frondationis sese evolventes; rhachi cylindrica serius siccata sub-
plana) foliolis approximatissime oppositis v. rarius alternis omnino
ob arctissimam marginum revolutionem lineari-filiformibus apice
mucrone robusto aculeiformi pungentissimo terminatis, marginibus
integris acus recte simulantibus.
Coni ¥ et 2 nobis hucusque ignoti.”
1 Using a screen of ammoniacal copper sulphate which lets through a good deal
of green as well as the blue end of the spectrum.
2 “The Wealden Flora”’ (Catalogue of the Mesozoic plants in the British Museum),
vol. 11. 1895, p. 22, Pl. 111. fig. 3.
3 ibid. Pl. m1. fig. 6.
4 Lemaire, C., “L’illustration horticole,” Journal spécial des serres et des jardins,
vol, x1v. 1867, p. 80.
341
Bisa res gears
L
Y 7, Vy
Mr Seward, On Encephalartos Ghellinckuy, etc,
1897.]
Nat. Size.
1
iat
ARTOS GHELLINCKII, LEM.
ENCEPHAL
2
28
4 i : ? SS aes preteen ee stem teens rem avrnsiw,
1897.] Mr Seward, On Encephalartos Ghellinckii, etc. 343
Lemaire describes both H. villosus and EF. Ghellinckii, and
speaks of the two species as quite distinct from the other members
of the genus. The two woodcuts and the coloured plate which
accompany the above diagnosis convey an imperfect idea of the
appearance of the latter species’.
The plant reproduced in the Plate? was obtained by Mr Lynch,
of the Cambridge Botanic Gardens, from Messrs Sander and Co., of
St Albans, who received it from the interior of the Province of
Natal. When sent to Cambridge the stem shewed no sign of life
_ and bore traces of having been considerably charred, probably in
a forest fire. After lying for some months in an apparently dead
condition a fine crown of leaves was produced, and the accom-
panying photograph was taken before all the fronds had attained
their full development. The stem measures about 28 cm. in
height and 70 cm. in circumference, and is covered with the
characteristic armour-like investment of persistent and corky leaf-
bases. The leaves are a little over 90 cm. in length, and in those
which are not fully expanded the slender apices are bent over
at the tip, and the linear-filiform pinnae are crowded together like
the barbs of a goose-quill. The rachis of the mature frond bears
two rows of opposite or alternate pinnae, about 11 cm. in length
and 2 mm. broad, which are attached laterally to the leaf axis.
- Both the rachis and pinnae present a woolly or tomentose appear-
ance, especially in the young condition. The pinnae terminate
in an acute spinous apex, and the margins are strongly revolute ;
four parallel veins traverse each pinnae, but these are hardly
visible in a surface-view. As shewn in the plate, the two rows of
pinnae form a fairly wide angle with one another, and are not
extended in one plane. In some of the fronds the rachis is
slightly twisted in a spiral, as in Macrozamia spiralis, Maiq.
The general appearance of Encephalartos (hellinckw suggests a
distinctly xerophytic habit, and this is borne out by the thick
cuticle and sunken stomata of the pinnae.
The rachis is traversed by numerous vascular bundles of the
typical mesarch form, characteristic of the petioles and peduncles’
of recent Cycads. Each bundle is surrounded by a more or less
complete ring of large thick-walled fibres; the parenchymatous
ground-tissue contains several large mucilage canals and the
hypoderm consists of strands of fibrous elements alternating with
parenchyma. The anatomical characters agree with those of
other Cycads, and especially with other species of Hncephalartos.
A transverse section near the tip of a rachis bears a striking
1 Lemaire, loc. cit., vol. xv. 1868, Pl. 567.
2 The photograph reproduced in the plate was taken for me by Mr Hayles of the
Cavendish Laboratory.
3 vide Scott, D. H., Annals of Botany, vol. x1. 1897, p. 399.
344 Mr Seward, On Encephalartos Ghellinckii, etc. [Nov. 8,
resemblance, in the scattered collateral bundles and large canals,
to the fossil petioles known as Myeloxylon. ‘The hypoderm in the
younger portion of a rachis consists in part of collenchyma, which
afterwards developes into uniformly thickened fibrous tissue.
The following points may be briefly noticed in the anatomy of
the pinnae. In tranverse section a pinna has the form of a
somewhat flattened crescent, the two edges bemg bent over
towards the under surface. The upper surface is covered by a
thick cuticle, and the epidermis is succeeded by two or three
layers of thick-walled fibres, and internal to these there is exceed-
ingly well-marked palisade tissue of one layer of long cells;
internal to this the mesophyll consists of spongy parenchyma
followed by one or two rows of fibres and the lower epidermis.
There are numerous stomata on the lower surface, the two guard-
cells being situated at the bottom of a fairly deep depression. The
mesophyll is traversed by four collateral bundles surrounded by a
ring of fibrous elements. The woolly appearance of the young
fronds is due to the occurrence of numerous long unicellular hairs
borne on a short and thick-walled stalk-cell as in Dzivon edule,
Lind., and other Cycads1.
The importance of such a species as Encephalartos Ghellinckia
in connection with fossil Cycads has previously been discussed.
The necessity of examining as many recent species as possible,
especially the less known and rarer forms, cannot be too strongly
urged. ‘There are several fossil fronds in which the rachis bears
numerous long and narrow pinnae, which may well be compared
with Encephalartos Ghellincku. Some of the Mesozoic fronds,
which have been erroneously referred to the genus Cycadites?,
bear a very close resemblance to those African Cycads with the
narrow linear or linear-filiform segments.
1 My thanks are due to Mr A. W. Hill, of King’s College, for preparing several
sections of the frond of Encephalartos Ghellinckii and other species.
* For references to fossil fronds vide Wealden Flora, vol. 11. pp. 36 et seq.
1897.] Mr Townsend, Electrical Properties of Gases. 345
Monday, 22 November, 1897.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
The following communications were made to the Society :—
Q) Partial Differential Equations of the Second Order. By
Professor ForsyTH.
This paper is printed in the Transactions, Vol. xvi. Part 11.
(2) Electrical Properties of Newly Prepared Gases. By
JOHN S. TowNnsEND, M.A., Cavendish Laboratory, Cambridge.
(1) The experiments which are described in this paper form
a continuation to those which have already been published in the
Proceedings of the Cambridge Philosophical Society, Vol. 1x. Pt. v.
It was there shown that the gases given off by the electrolysis of
sulphuric acid or caustic potash carry with them an electric charge,
a large percentage of which remains in the gas after it has been
bubbled through a liquid, and passed through glass wool to remove
the spray. Another property of these gases is their power of con-
densing moisture to form a cloud. No such cloud could be observed
in newly prepared gases unless they were charged, and further the
weight of the cloud was found to be proportional to the charge on
the gas. These results go to show that the condensation of the
moisture is connected with the charge, and the experiments
described in section 16 of the above paper, and in section 19 of
this paper prove that when the cloud is formed in a charged gas
the electrification resides on the drops forming the cloud. So that
we have definite proof of the fact that the drops are formed round
the carriers of the electric charge.
(2) These results were used to find the charge on each carrier,
and it was found to coincide with what we can calculate as being
the atomic charge, on the supposition that at ordinary temperature
and pressure there are 10” molecules in each cubic centimetre of
a gas. The experiments giving the weight of the cloud corre-
sponding to the charge being of importance, were repeated by the
following method which gave the same proportionalities in the
different gases between the charge per c.c. and weight of cloud
per c.c., as were previously obtained.
(3) The apparatus which was used is shown in figure 1. The
positively charged oxygen and hydrogen given off from a dilute
346 Mr Townsend, Electrical Properties of [Nov. 22,
sulphuric acid cell were first bubbled through a solution of potas-
sium iodide in the small flask A and then through distilled water
Fie. 1.
Insulators are drawn with dotted lines and conductors with continuous lines.
in B. Both A and B were immersed in a trough of water C so
that they should remain at a fixed temperature while an experi-
ment was being conducted. The charged gas thus formed a cloud
and carried it along the delivery tube B, which led into the
paraffin block P inside a large metallic screen S. The block P
was arranged as shown in the figure in order that the moisture
should not break down the insulation by settling on the paraffin.
By this means the moist gas. entered the larger tube 7’ connected
to three sulphuric acid bulbs F set up between the two paraffin
tunnels P and Q. After the gas had bubbled through the acid
it was not only cleared of the moisture, which under ordinary
conditions it would have carried from B, but the cloud was also
completely removed. The increase of weight in the bulbs thus
arises from two causes, and when the weight of the moisture
necessary to saturate the volume of the gas which passes through
F is subtracted from the total, the weight of the cloud is obtained.
The gas on leaving F entered one of the insulated inductors, the
smaller one G being used for oxygen, and the larger one J for
hydrogen. The inductor and the bulbs were both covered with
tinfoil and connected to mercury cups in the paraffin block R, so
1897.] Newly Prepared Gases. 347
that either of them could be readily connected to the insulated
quadrants of the eloctrometer.
The experiments were conducted in the following manner.
The sulphuric acid bulbs were carefully weighed and then con-
nected by indiarubber tubing to the glass tubes which were
imbedded in the paraffin blocks as shown in the figure. The
current through the cell was switched on for a few minutes before
joining the bulbs into the series, so as to drive the air out of A
and B. As soon as the gas began to bubble through the acid in
F a stop watch was started. By connecting the conductors F and
G alternately to the quadrants of the electrometer the rate at
which each was acquiring a charge was found. The sum of the
charges acquired by #’ and G denotes the total charge passing out
of B and that acquired by F# divided by the total is the dis-
charging power of the bulbs. After the stream of gas from the
cell had been running through the apparatus for a sufficient time
the bulbs were removed, and dry air was drawn through them
before weighing them a second time. In each experiment a
current of 14 amperes was used which was kept constant by
having an ammeter and an adjustable resistance in the circuit.
In order to reduce the readings on the electrometer scale to
absolute units it was found that when F was connected to the
quadrants and the other conductors to earth, each scale division
represented ‘0040 electrostatic units of quantity, and when G was
connected to the quadrants the scale divisions each represented
0036 electrostatic units. The inductor J which was used with
hydrogen had a larger capacity than either of the other two con-
ductors, and when it was connected to the quadrants it required
‘0042 electrostatic units to make the spot of light on the electro-
meter scale move through a division.
The following tables give the results of the experiments which
were made with the different gases, @ is the temperature in
degrees centigrade of the water in B, W the increase in the weight
of the sulphuric acid bulbs, and n, and n, the numbers of divisions
that the spot of light on the electrometer scale moves per minute
when F' and G [or J] are connected to the insulated quadrants ; w
is the calculated weight of the moisture necessary to saturate the
volume of gas uv at temperature @ which passes through Ff’ in the
course of the experiment, ~ the weight of the cloud per c.c.,
v
and p the charge per c.c. on the gas. The volume 2 is easily cal-
culated as the gas is evolved by a known current.
Table I. gives the results obtained with positive oxygen. In
each experiment a current of 14 amperes was used, and the stream
of the evolved gas passed through # for 20 minutes.
348 Mr Townsend, Electrical Properties of — [Nov. 22,
Table II. gives similar results for positively charged hydrogen.
Table III. refers to negatively charged oxygen from a caustic —
potash cell, the stream of gas being passed through F for 15
minutes in each experiment.
The experiments were performed with widely different densities
of electrification p, in order to find how the weight of the cloud
varied with the electrification. The ratio of the weight of the
Dwein given in the last column for
‘cloud to the electrification
each experiment. The variations in p were obtained by varying
the temperature of the cell from which the gas was given off.
Both in the case of a sulphuric acid electrolyte and a caustic
potash electrolyte the charge on the gas which is evolved by a
given current increases as the temperature of the electrolyte is
raised.
TABLE I. + Oxygen from H.SO, electrolyte.
W-w
v p pv
l 22 31 | -0270 || 0050 | 22:3 x 10 §| 4:04 x 1077/55 x 10
1 13 20°, | :OTS87 1/0050 | T4511 1052 | 2-53) 1052-4 te
13 21 30 =| -0330 || 0118 | 20-8 x 107§|3°8 x 10°?|5:5x 10%
14 9 19 | :0240 || 0125 |11°5 x 10-°| 2:05 x 1073] 5°6 x 10°?
TABLE II. + Hydrogen from H.SO, electrolyte.
W-w W—-—w
2 oy) Pp pu
O | 21:5 28-5 -0264 | 0092 | 8:8 105°) 2:1 x 105°) 4-25 alee
Oo |) ae 34 | -0296 || 0092 | 10-5 x 10-°| 2:57 x 10°*| 4:1 x 10%
15 32 | 37 | 0486 || 0264 | 10°8 x 1075) 2°8 x10) 3-8x 10°
| 15-3] 26 31 | -0445 ||-0271 | 85x 10°°|2:2 x10°%)39x 10%
1897.] Newly Prepared Gases. 349
Taste IIL. —Ozygen from KOH electrolyte.
W-w W-w
v P pv
0 15 266. | -OL8S8.)-0085. | 21x 105% |3°1 x 10-*| 6:8x 10%
O | 22 32 | -0217 | 0035 | 25x 10-° | 4-1 x 107*/ 6-1 x 10-°
12 14°5| 24-5] -0230 || 0081 | 20x 10-6 | 2°86 x 10°*| 7:0 x 10°
11:5] 12:5] 22:5}-0206 | -0078 | 17x 10-* | 2-51 x 10-3| 6-8 x 10-8
(4) The numbers given in the tables show that in each case
the weight of the cloud is proportional to the charge, and that this
proportionality does not vary with the temperature of the water
from which the cloud is formed, at least within the limits of 0° and
14°C. The ratio is not so exact in the case of the negative oxygen
as it is for the other gases. The only chemical difference that was
detected was that the former were slightly acid and the latter
alkaline in their reactions. Since the vapour rising from hot
caustic potash does not change red litmus to blue, the alkalinity of
the gas must be due to small particles of caustic potash which are
carried with the gas from the electrolyte and give it an alkaline
reaction even after bubbling through sulphuric acid, this could
easily be detected at all temperatures of the cell by letting the
oxygen or hydrogen pass along a tube with red litmus.
The oxygen given off by the electrolysis of caustic potash has
no appreciable charge till the temperature of the cell is up to
about 20° C. and the cloud begins to appear at the same time as
the charge on the gas, so that the presence of the alkaline spray
can have only a very small effect as no cloud is observed in the
oxygen coming from the cell at a temperature 10° C. although the
presence of the spray of caustic potash can be easily detected.
(5) The following simple experiments show how intimately
connected the charge on the gas is with the formation of the
cloud.
The apparatus used is shown in figure 2. The oxygen given off
by a current of ten amperes from a caustic potash cell of specific
gravity 1:3 was bubbled through a solution of potassium iodide in
the flash A to remove any traces of ozone. Before entering the
inductor J the gas bubbled through water in B. The inductor I
was insulated and connected to the quadrants of the electrometer
so that the charge on the gas that entered it could be read off on
350 Mr Townsend, Electrical Properties of [Nov. 22,
the electrometer scale. The gas was not passed through any glass
wool before entering J so that as much spray as possible should be
carried from the cell.
tee
Fic. 2.
The cell was at a low temperature, 11° to start with, and a
current of 10 amperes was switched on which gradually warmed
the electrolyte. During the first nine minutes that the current
was on and the gas entering the inductor, no electrification what-
soever was detected, and no cloud could be observed over the water
in B. During these nine minutes the temperature of the cell ©
rose from 11° to 18°.
During the next five minutes a deflection of 9 divisions
negative was obtained and the temperature of the cell had risen
to 21°5.
At a temperature between 22 and 23 a thin cloud began to
appear over the water in B and the spot of light was then moving
at the rate of 4 divisions per minute, so that before the cloud
becomes distinctly visible a small electrification of about 2 x 10
Electrostatic units per cc. is necessary. When the current is
continued and the cell becomes hotter the electrification on the
gas increases and the cloud becomes denser.
(6) In order to show that the cloud disappears when the
charge on the gas is removed the temperature of the cell was
raised to 48° and, with the same apparatus as was used for the
last experiment, the three following results were obtained.
(a) When the gas passes from the cell to the inductor with-
out filtering through glass wool a dense cloud was observed over
1897.] Newly Prepared Gases. 351
the water in A, and a deflection of 29 divisions negative per
minute was obtained as the gas entered J.
(b) The tube connecting A and B was removed and a tube
containing glass wool was substituted. With the same current
through the cell a slight cloud was seen over the water in B and
the deflection was reduced to 6 divisions per minute. The elec-
trification of the gas was thus reduced to 1 of its original value
by passing through 15 centimetres of glass wool. The amount of
spray carried through this length of wool must have been ex-
tremely small but the cloud was distinctly visible.
(c) The tube containing the glass wool was heated with a
Bunsen burner, and its discharging power was considerably
inereased as the spot of light then gave only 2 divisions per
minute and no cloud was observed over the water in B.
It is thus evident that the formation of the cloud and the
presence of the charge are phenomena which accompany one
another.
(7) The clouds which are formed are slightly different in
appearance and for equal electrifications those formed in oxygen
are whiter than those formed in hydrogen. A difference is also
to be noticed in the positive and negative oxygen clouds, that
formed in the latter being the whiter. This would point to the
fact that the drops formed in the negative oxygen are larger than
those in the positive, and that those formed in either positive or
negative oxygen are larger than those in the hydrogen. A fairly
approximate value for the radius of the drop may be obtained by
observing the rate at which the cloud falls in a vessel. The
velocity of the drop through the gas was obtained by taking two
photographs of the cloud allowing some minutes to elapse between
the two exposures. Figure 3 represents two such photographs
taken of the cloud formed by bubbling the charged oxygen from
a sulphuric acid electrolyte through water. Three minutes were
allowed to elapse between the two exposures, and the scale shows
that in that time the cloud had fallen between 9 and 10 milli-
metres. Similar experiments were made with the other gases,
but in the case of the hydrogen the outline of the cloud never
became so distinct as it did in the oxygen.
The sizes of the drops were obtained from the formula
paV = 47a'g (Lamb, Motion of Fluids, p. 229).
This gives. for the radius of the drop in the positive oxygen
68 x 10~, the rate of fall being 10 millimetres in 3 minutes, and
the radius of the drop in negative oxygen 7-9 x 10-* the rate of fall
being 18 millimetres in 4 minutes,
352 Mr Townsend, Electrical Properties of — [Nov. 22,
We thus know the weight of each drop and dividing this into
the weight of the corresponding cloud, we obtain the number of
drops per cubic centimetre.
Fic. 3.
When the number of drops is divided into the charge per cubic
centimetre the charge on each is obtained.
The charge on the positive carrier was thus found to be
2-4 x 10”, and that on the negative carrier to be 2°9 x 10™°. When
we take into account all the experimental errors these two charges
may be considered equal and approximately 3 x 10~". The charge
on the hydrogen was found to be between one-third and two-
thirds of this value but could not be arrived at very accurately
owing to the difficulty of finding the size of the drop. For present
purposes this charge will be taken as 3 x 107. 5
Velocity of the carrier when acted on by an electric force.
(8) It has been shown that the radius of the drop forming the
cloud is in the case of negatively charged oxygen 810~, so that
its weight is 210~" grammes and when acted on by gravity, it
moves at the rate of 18 millimetres in four minutes. The force
acting on the drop is practically 210~°, so that it would require
210°
3x 10"
velocity, or 2000 volts per centimetre. As we are only dealing
an electric force of absolute units to produce an equal
1897.] Newly Prepared Gases. 353
with small electromotive forces it is evident that we may disregard
the effect of mutual repulsion of the carriers when the gas is
carrying a cloud. When the gas is bubbled through sulphuric
acid the radius of the carrier is so much reduced, that the effect
of the mutual repulsion of the particles carrying the charge is
easily detected.
(9) The following is a general method of investigating the
motion of a gas in a vessel of any shape, the initial distribution
being uniform. Let p be the density of electrification in any part
of the gas, uv, v and w the velocities of the carriers along the axes
of x, y and z.
; : ONE ERE) a! RPA ATs
The equation of continuity is ; hanes es dy oe =0, the
notation being the same as that used in Lamb, Motion of Fluids.
Let ¢ be the electric potential; — a — ek and — Ste , are the
da dy dz
forces which act on the charged carriers, and their velocities w, v,
and w, are given by the equations :—
dg | dg | ‘4
(1) Kua ea: Ei — ae Kw=— e—*
where e is the charge on the carrier and « is a constant to be
determined experimentally.
Substituting these values for w, v, and w, in the equation of
continuity and we obtain :—
ele = V2 = V2 ae.
54 é 1) 0, but ti) = Aap,
therefore = St = — 4rre.
Integrating and we obtain :—
Po
(2) Pp Ee ees eee 5
ies —
where p, is the initial density, which is uniform throughout the
space considered.
Equation (2) shows that the motion takes place in such a way
that the density p is a function of the time only and does not vary
from point to point in the gas, on this account no variation in
the pressure of the charged gas takes place and the terms = : = f
BO4 © Mr Townsend, Electrical Properties of — (Nov. 22,
and z :
ing with the motion of gases, can be omitted in equations (1) since
p does not vary from point to point.
which have in general to be taken account of when deal-
When the gas is in a closed vessel the mutual repulsion of the
carriers of the electricity drives them to the sides where they
either remain so close to the walls that they cannot be blown out,
or else get discharged against the sides. The charged gas
remaining in the vessel has a uniform density given by equation
(2), and if the vessel which contains it is an insulated conductor
connected to a pair of quadrants of an electrometer the deflection
on the electrometer scale will be proportional to p when the charged
gas is blown out of the vessel.
(10) In order to investigate experimentally the rate at which
the gas loses its charge to the sides of an inductor, or in other
words to find how the density p will vary with the time, a metal
Fic. 4.
cylinder C, figure 4, 30°2 centimetres long and 1°6 centimetres in
diameter, was used. The two ends of the cylinder fitted into
paraffin blocks P, and P;, into which were also fixed the glass
1897.] Newly Prepared Gases. 355
tubes 7, and 7. The tube 7;, through which the cylinder was
filled, had several layers of fine copper gauze across the broad
end, which tended to distribute the gas evenly across the section.
The whole apparatus was contained inside a screen S, the ends A
and B of the tubes leading to the cylinder projecting outside the
screen ; by this means the charged gas could be blown out of the
cylinder, without stirring any apparatus or tubes inside S; so that
the deflection on the electrometer scale, when C' is connected to
the insulated quadrants, was solely due to the removal of the
charge inside C. Any effect of gravity, on the motion of the
carriers towards the sides of the tube, was prevented by placing it
in a vertical position.
(11) The gases that were examined were the oxygen and
hydrogen given off by electrolysis of dilute sulphuric acid. The
cell was raised to a temperature about 20° above the room, at
which it could easily be kept by running the current. By means
of an ammeter and variable resistance in the circuit the current
could be kept constant. A method is thus provided of filling the
cylinder several times with a gas having a constant electrification
per c.c. When filling the cylinder with the hydrogen it is best
to lead the gas in at the top, and when using oxygen at the
bottom, in order that the air may be driven out in as short a time
as possible, as it is not desirable to run the current for more than
five minutes at a time, when a number of experiments have to be
performed requiring the same electrification in each case.
The gases were first bubbled through potassium iodide; and
then through strong sulphuric acid, so that they should enter the
tube D perfectly dry. The cylinder and tubing connected with it
were thoroughly dried by heating them with a Bunsen burner and
then blowing dry air through. This precaution is absolutely
necessary as it only requires a very slight amount of moisture to
form a cloud, and this would impede the motion of the carriers.
(12) A series of experiments of the following type were then
performed: The cylinder was connected to a pair of quadrants of
the electrometer, which were kept to earth while the cylinder was
being filled and insulated before blowing out the gas, so as to get
the readings on the same part of the scale. The tube A was
closed, and D connected to the delivery tube of the sulphuric acid
wash-bottle, and a current of 14 ampéres sent through the cell.
It only required the current to run for about five minutes to com-
pletely fill C with the charged gas. The circuit was then broken
and the tube B closed. At the same time a stop-watch was
started. After the lapse of ¢ minutes the ends A and B are
opened, and dry unelectrified air blown through C' to expel the
VOL Lx, Pl Vill 29
356 Mr Townsend, Electrical Properties of — [Nov. 22,
charged gas; this caused the spot of light on the electrometer
scale to move n divisions, which is proportional to p the density of
the electrification after the gas has remained in the cylinder for a
time f.
The numbers thus obtained for n and ¢ are given in Tables I.
and II., the first being for charged hydrogen and the second for
charged oxygen.
nN t
Selena a n t
32 0 mie
AQ ~ 0
25:5 1
37:5 2
20:5 2
TABLE I. TABLE ik 29-5 4
175 3
24-5 6
15:5 4
22, 8
14 5
It will be seen that these numbers are nearly exactly the same
as those given by the formula Dare if we put nm = 32 and
6 =-0043 in the case of the hydrogen, and n,=49 and @='00255
in the case of oxygen. The numbers calculated from this formula
are given in the two following tables:
n t
SSS n t
32 0 Pohl be
49 0
25-4 1
37°5 2
21-1 2
TABLE IIT. TABLE LV. 30-3 4
18 3
25-5 6
15-7 4
Dy) 8
14 5
1897.] Newly Prepared Gases. 357
This shows that p=... Hence we have from equation (2)§ 9
ioe a), 4d
Amr pve
Dae
(13) The velocity of the charged carrier when acted on by an
electric force can be found from the above numbers. The electro-
meter having been standardized, it was found that ‘0037 electro-
_ static units of quantity would give a deflection of one division on
the scale, so that we get
32 x 0037 ns pee
poe 8K B02 Le
in the hydrogen experiments, and
49 x ‘0037 =
po ax xBODT
in the oxygen experiments.
Let «z and e;, denote the values of « and e for hydrogen and
Ko and é, similar values for oxygen, and we get
eile =°0043, where p, = 2°10-%,
AT
and apm 00255, where p)=3'10~.
Ko
Hence S56 atl als cane oopseneneeh (1).
H 0
From the equation «V = Fe, which is similar to the equations
(1) § (9), V being the velocity due to an electromotive force F,
we obtain for the motion of the charged carrier in hydrogen
F
V= BG?
and for the motion of the charged carrier in oxygen
F
= 5°
Hence under an electromotive force of 1 volt per centimetre,
: 1 ;
the hydrogen carrier travels at the rate of 300 x56 centimetres
29—2
358 Mr Townsend, Electrical Properties of [Nov. 22,
: é 1 1 2
per second, and the oxygen carrier at the rate of 300 * IB centi-
metres per second.
The conclusions arrived at from the above investigations are
based on the assumption that in each case we are dealing with a
gas containing carriers all charged with the same sign, either
positive or negative. Experiments on conductivity have been
carried out in order to test this point, and it has been found that
we are in reality dealing with mixtures. Thus in the case of
oxygen, or hydrogen, from a sulphuric acid cell having a positive
charge equal to 8e, it is possible to obtain from the gas a positive
charge of 4e and a negative charge of e. If we suppose the positive
and negative to act independently the charge on the oxygen
carrier would be 510-” instead of 310; also the velocities under a
volt per centimetre would be smaller in the ratio of 3:4 than
those given above.
We can arrive at an approximate value to the size of the
carrier if we assume that the viscosity of a gas effects the motion
of a small sphere and a large one according to the same law
6rpaV = P.
(Lamb, loc. cit.). Substituting
1
Vane
NO
for hydrogen, and
igs HOt aceon ee
= — = TS S= 1 712
300 2) aa
we get the radius (a) for the hydrogen carrier 45107. Similar
substitutions give the radius of the oxygen carrier 121077. Hence
the carriers are large compared with molecular dimensions.
JP
The velocities obtained for the carriers in the conductivity due
to Réntgen rays are far greater than the above. Thus for oxygen
and hydrogen Mr Rutherford obtains velocities of 5:2, and 1°4
centims. per second under a volt per centimetre. [Phil. Mag.,
Nov. 1897. ]
If we assume that the charges on the carriers are of the same
order as those obtained in § 7 we see that the dimensions of the
carrier are smaller than those with which we are here dealing.
1897. ] Newly Prepared Gases. 359
The discharging power of tubes.
(14) It has been shown that, if the gas with a uniform charge
po per c.c. be left in a tube for a time ¢, the density of the electri-
fication falls to a uniform value p, given by the equation
where a is a constant. Now if we suppose that the velocity of a
gas as it passes along a tube be perfectly uniform and that no dis-
charging takes place due to accidental circumstances, the values of
t, p, and p,, would be connected by the same equation, where now
t denotes the time that any portion of the gas takes to traverse
the tube, p, and p being the densities of electrification on entering
and escaping from the tube.
When the gas is given off by a current through an electrolyte,
the volume g which enters the tube per second is known when the
: a é
current is known; so that ¢=— where V is the volume of the
tube, and the above equation becomes
Po— Pp _ %p.V
p q
The values of p, and p are easily found and satisfy this equation
roughly, so that a can be determined; its value however is greater
than = found already. This is due to accidental discharging, as
it can be shown that, even when the carrier is so large that the
small E.M.F. driving it to the side of the tube could have no
appreciable effect, still a measurable discharge takes place.
(See § 21.)
(15) If the gas be run into an insulated inductor after
traversing the tube, var is the ratio of the charge gained per
minute by the tube to the charge gained per minute by the in-
ductor. These charges can be easily found by connecting the tube
and inductor alternately to the insulated quadrants of an electro-
meter. The tube C insulated in the manner described in § 10 was
used in these experiments, the gas examined being the hydrogen
given off by a current of 14 amperes from a dilute sulphuric acid
electrolyte. The following deflections n, and n, were obtained, n,
being the deflection per minute when the tube is connected to the
360 Mr Townsend, Electrical Properties of — [Nov. 22,
insulated quadrants, and n, the deflection per minute when the
inductor is connected to the insulated quadrants.
fi |)
Lene
9:5| 36
The relative value of n, and n, in absolute units of quantity
was 12: 13°5, so that
Po—p _ 12m
on BSE
We thus obtain the following numbers showing the connection
Po P
between and pp, so that PoP is (within 5 per cent.) pro-
portional to the densities of the electrification.
Po=P ose
p ee PPo
30 He Meee 1510)
Joel AO Oss) alo
(16) Similar values were obtained for p)—p and p for the
oxygen given off from the same electrolyte by a current of 14
amperes. A different method was used in this case, which did not
require an inductor. When the tube C (experiment § 10) was
being filled with a charged gas, which enters with an electrification
p, and escapes with an electrification p, the quantity p, — p can be
obtained by observing the rate (m, per minute) at which the spot
of light moved on the electrometer scale, when the tube is full of
the charged gas, and the stream kept running through it. The
mean density of electrification in the tube is practically pe ;
and was obtained by blowing out the charged gas, and observing
the deflection », which is proportional to ore x V, where V is
1897.] Newly Prepared Gases. 361
the volume of the tube. The following values of n, pad MN, Were
obtained :
The rate q at which the gas is supplied to the tube is ‘85 c.c.
per second: so that (p,—p) x 51 is the charge given to the tube
per Aaa as the gas passes through it, and is proportional to ,,
and Pot 2 Px Vis proportional to n,, where V, the volume of the
tube, is 60°4 cubic centimetres.
Thus we get the following values for ?°—? and Pu:
(17) The ratio PoP was also found to increase when the
current through the electrolyte diminished, thus showing that the
ratio depended upon the rate at which the gas is supplied to the
tube. Another tube of equal length and 1:12 centimetres in
diameter was examined by similar methods, and it was found to
have a far less discharging power than the larger tube; so that,
when the supply g and density p, are given, the smaller the bore
of the tubing that is used to convey the gas from one vessel to
another, the less will be the loss of the charge. The above results
showing the dependence of cai on p, are important as we see
from the formula
Eee ames opal
P K q
that the increase in the charge due to heating the cell arises from
an increase in the number of carriers with the same charge, and
362 Mr Townsend, Electrical Properties of — [Nov. 22,
not from an increase of the charge on the carriers already present ;
for, if the increase in density were due to an increase in p, we
would have found ?° : P to be proportional to the square of py.
(18) It would be almost impossible to arrange to pass the gas
along a tube in such a way that the discharging power would be
as small as the theoretical value, calculated from the numbers
given for «, section 13. Small differences in temperature between
the gas and the sides of the tube, and other effects which would
give rise to currents in the gas, considerably increase the dis-
charging power, but have a comparatively small effect on the loss
of charge when the gas is allowed to stand in the tube. The
velocity of the carrier towards the sides of the tube, due to an
electromotive force, will on this account be too large when calcu-
lated from the formula 2°? = ie : pol
p
eer
Thus, when we substitute the values given in §§ 10, 11 for
Po and Po, We obtain for K the values:
Keo.
IK = NS 5 Oa:
Causes which influence the discharging power.
(19) Inthe above experiments the gases were always treated in
the same way before entering the tube C, being bubbled first through
a solution of potassium iodide and then through strong sulphuric
acid. When the gases are bubbled through water instead of sul-
phuric acid they will enter C carrying with them a cloud, the
effect of gravity upon which makes itself very apparent by com-
paring the charges acquired per minute by the tube, when in the
vertical and horizontal positions. Thus in the case of a stream of
highly charged hydrogen, which bubbled through water before
entering C, it was found that the charge acquired was 14 scale
divisions per minute as the gas passed through C’ in the vertical
position; and 47 divisions per minute with C in the horizontal
position. The electric capacity of the conductor, consisting of C
and the quadrants, was vot altered by more than 3 per cent. by
turning the tube round; so that the large increase in the dis-
charging power must have been caused nearly entirely by the
force of gravity acting on the drops forming the cloud. The
experiment shows that the charge resides on the drops forming
the cloud.
1897.] Newly Prepared Gases. 363
A similar result was obtained in the case of charged oxygen
carrying a cloud; the corresponding numbers of divisions of the
_ scale being 4 and 20, showed that five times the charge is
removed by the tube when it is turned from the vertical to the
horizontal position.
Rough values for the size of the drop might be deduced from
these numbers; but the variations in density per c.c. (due to the
cloud) are so great, that it would be impossible to arrive at
satisfactory values, especially in the case of hydrogen, where the
weight of the cloud can be as great as 4th of the weight of the
gas in the same volume.
(20) Even when the gas has been bubbled through sulphuric
acid before entering C,a slight effect of this kind is still to be
found. Thus, when the tube is turned from a vertical to a
horizontal position, the charge acquired by it per minute increases
from 16 to 19 divisions of the electrometer scale per minute.
If the coefficient of viscosity can, even roughly, be applied as in
section 13 to determine the size of the carrier, the effect of gravity
could not exert on a carrier a force that would cause it to move
through the gas surrounding it, with a velocity of the same order
as z4, centimetres per second. In fact, if we take the density of
the carrier to be unity, its radius should be as big as 3107, in
Uae that the force of gravity should make it move with a velocity
zap Centims. per second.
But if, instead of considering a single carrier, we consider the
case of a finite quantity of gas (occupying unit volume say), as
differimg from the surrounding gas by ‘05 per cent. in density,
which could arise from various causes, a vertical motion far greater
than the above would ensue, which would affect the discharging
power of a horizontal tube.
The gases can be sent through a tube containing phosphorous
pentoxide, after bubbling through sulphuric acid, so as to remove
all traces of moisture; and if the powder is placed loosely in a
horizontal tube, about 8 centims. long with glass wool at the end
to prevent dust being carried along, not more than half the charge
on the gas will be lost. The hydrogen when dried in this manner
loses more of its charge, in passing along the vertical tube C, than
if it had been dried by sulphuric acid alone; but the loss of
charge was not found to be increased by turning the tube from the
vertical to the horizontal position.
(21) The discharging power of a tube in a vertical position is,
as we should expect, greatly diminished by having the gas moist,
as the electric force is then too small to have any appreciable
effect in causing the drops to move towards the sides.
364 Mr Townsend, Electrical Properties of [Nov. 22,
Thus, in an experiment similar to that explained in section 15,
the hydrogen, instead of being bubbled through sulphuric acid
before entering C; was bubbled through water, and it was found
that when C acquired a charge of 14 per minute the inductor
acquired 75 per minute, whereas if a similarly charged dry gas
were used, C’ would have acquired a charge at the rate of 28 per
minute, and the inductor at the rate of 62.
The same property holds in the case of charged oxygen.
Thus when the gas carries a cloud only 4 divisions per minute
were acquired by C, whereas a similarly charged dry gas would have
given 7 divisions per minute. The loss of charge of the clouded
gas in passing through a vertical tube is due to the unevenness
in the motion and the accidental contact of the cloud with the
sides.
Diffusion.
(22) Experiments were performed on the diffusion of charged
gases in order to find out whether any of the charge can pass ~
Fic. 5.
through porous earthenware. The apparatus which was used in
these experiments is shown in figure 5. It consists of two
1897.] Newly Prepared Cases. 365
cylinders, the outer Q was of tin, and the inner P was a porous
porcelain vessel fixed by means of corks (C) to the tin cylinder.
The porous vessel had one aperture which was fitted with an
indiarubber stopper carrying two tubes projecting through
the sides of Q@ at D, and D,. The tube Z was broken, and
fitted with a paraffin tunnel for purposes of insulation, and the
tube U dipped into a sulphuric acid bottle and so acted as a
manometer.
The outer cylinder had two apertures at H and F, the tube R
from # led into a large insulated inductor, and the tube from F
was connected through a paraffin tunnel to the delivery tube of
a sulphuric acid bottle. e
Before performing an experiment it is necessary to thoroughly
dry the whole apparatus, this was done by blowing dry air through
T and F. The charged hydrogen from a sulphuric acid electrolyte
was dried and allowed to enter the cylinder P through 7.
The bellows is connected to the tube S and a gentle current
of air is blown into the cylinder through F. The cylinder Q is
connected to earth, and the inductor into which R leads is con-
nected to the insulated quadrants of the electrometer. By this
means the hydrogen which diffuses through P is carried with the
air current along the tube R into the inductor. The sulphuric
acid in U during the course of the experiment rose in the tube
showing that the hydrogen diffused as quickly as the tube 7
supplied it.
Only a very small fraction of the original charge was found to
be on the gas after diffusion as the deflection per minute, as the
diffused gas enters 7, was found to be less than 2°/, of the deflec-
tion obtained by allowing the gas to enter J directly.
(23) Having seen that the hydrogen in diffusing carries with
it no appreciable charge it is interesting to know whether the
electricity is carried to the sides and gets caught in the pores of
the porcelain or whether the carriers remain distributed through-
out their original volume surrounded by the air which diffuses
in to take the place of the hydrogen.
In order to test this the whole apparatus was insulated and
experiments were conducted as follows :—
The outside cylinder Q was connected to the insulated quad-
rants of the electrometer, and the hydrogen from the cell after
bubbling through strong sulphuric acid was admitted into P by
means of the tube 7. The draught of air between P and Q was
maintained in order to make the diffusion as rapid as possible, no
inductor was used so that the hydrogen after diffusion was carried
366 Mr Townsend, Electrical Properties of — [Nov. 22,
into the atmosphere of the room through #. As the charged gas
entered P, the conducting cylinder @ being connected to the
quadrant, the deflection on the electrometer scale registers the
total charge that enters P.
When a sufficient charge had entered P, the tube 7 was closed
and the sulphuric acid in the manometer U rose rapidly and
showed a maximum difference of pressure between the atmosphere
inside and outside P of about 3 centimetres of acid. As the
blowing into # was continued the sulphuric acid in U began to fall
gradually and in a few minutes the difference of pressure was
reduced to one or two millimetres, which showed that practically
all the hydrogen had diffused out.
The question was then decided by observing what charge
could be blown out of P by blowing through 7, and it was found |
that a large fraction of the original charge could be thus removed
from inside P. The charge which is thus blown out does not
represent quite all the electricity left in the atmosphere in P
after the hydrogen had diffused out as about 10 per cent. got
discharged in bubbling through the sulphuric acid before escaping
through v.
The numbers obtained in three experiments which were per-
formed in the above manner are given in the following table :—
n, 1s the charge (in divisions of the scale) put into P, ¢, the time
in minutes required to admit the charge, h, the maximum height
in centimetres that the sulphuric acid rises in U after the tube 7
is closed, ¢, the time that elapsed while the manometer fell from
h, to h,, and n, the charge that was blown out of P.
Ny ty h, hy ty No
210 i 3 30 IL Ag 6 130
200 3 3°2 2 4) 125
132 5 30 2 4 98
The current through the electrolyte was in each case 14
amperes.
In the last experiment the charge on the gas was reduced by
passing it through a tube of phosphorus pentoxide before it
enters 7’.
We thus see that the carriers of the electricity in the charged
hydrogen can with ease be transferred to an atmosphere of any
1897.] Newly Prepared Gases. 367
other gas by diffusion. Also, by continuing the stream of hy-
drogen into P, the density of the charge in P increases, so that
diffusion not only affords a method of removing the charge from
a gas, but also gives us a means of increasing the electrification
per unit volume.
Experiments with hydrochloric acid.
(24) When gases are given off by electrolysis both the quantity
and sign of the electricity which they carry are affected by
various causes. These changes which the charge undergoes are
well illustrated by a series of experiments which were performed
with a 20°/, solution of hydrochloric acid.
The form of the apparatus used to generate hydrogen and
chlorine by electrolysis from hydrochloric acid is shown in
figure 6. It consists of two glass bulbs, joined together, from
each of which project two tubes S,, 7; and S,, 7,. The tubes
S, and S, acted as delivery tubes for the gases, which collected in
the spaces immediately underneath them. The electrodes, 4,
and #,, consisted of carbon sticks which fitted into the tubes 7;
and 7; indiarubber tubing projecting over the ends of 7 and 7,
prevented the apparatus from leaking when the bulbs were filled
with a liquid. The carbon sticks had a thin layer of copper
deposited on the ends A, so as to make good contact with the
mercury in the cups C,, C,. These cups acted as terminals to
which the leads, from the cells supplying the current, could be
joined. The current through the electrolyte was given by an
ammeter in the circuit, and was easily adjusted to any required
value by means of a variable resistance.
368 Mr Townsend, Electrical Properties of — [Nov. 22,
(25) The electric state of the gases was examined by leading
them into an insulated inductor, connected to one pair of quad-
rants of an electrometer. The other pair of quadrants, the case
of the electrometer, and the screen inside which the inductor was
placed, were connected to earth.
The hydrogen was bubbled through a strong solution of
caustic potash and the chlorine through water, before entering the
inductor.
(26) The charge carried by the hydrogen evolved from a
hydrochloric acid electrolyte varies in a very peculiar manner.
When new carbon electrodes are used and the current turned on,
the electrometer shows that the gas, at first, has a positive charge,
but although the current is kept constant, this charge diminishes
gradually and after some minutes becomes negative, 1t soon
reaches its maximum negative value and the charge then remains
constant, except for a small variation due to temperature. When
the electrolyte is cooled, and the same current again sent through
the acid, the hydrogen begins to come off with a negative
charge.
(27) The chlorine, which has been evolved from the positive
electrode, will be seen to have dissolved’in the acid not only round
the positive electrode, but also round the negative, before the
change of sign is observed in the hydrogen. If now this acid be
removed from G, and the electrodes well washed, and a fresh
quantity of acid used, it will be found that the electrometer will
indicate charges on the hydrogen, exactly similar to those at first
observed except that the positive charges are not so large.
After washing the electrodes a second time, and experiment-
ing again with a fresh quantity of acid, the same effect will be
observed without any further diminution in the positive charges.
The number of divisions of the scale obtained in an experi-
ment of this kind are :—
Ist minute 14 divisions positive,
[en 29 1 1 9 bb)
3rd is 5 *
after a few minutes the hydrogen came off with a negative charge,
corresponding to 5 divisions per minute. The current through
the electrolyte bemg 10 amperes, and the value of divisions on
the electrometer scale in absolute units of quantity, being obtained
by multiplying them by -003.
bP)
When the chlorine was similarly examined it was found to
have a small negative charge, corresponding to 4 divisions of the
1897. ] Newly Prepared Gases. 369
electrometer scale per minute. It did not vary in sign like the
charge on the hydrogen.
(28) It is probable that the remarkable change of sign that
occurs in the charge carried by the hydrogen is due more to the
absorption of chlorine gas by the carbon electrode, than to the
presence of chlorine gas in the electrolyte; for if the platinum
electrodes were used the hydrogen was given off with a large
positive charge and did not change when the chlorine got dissolved
in the electrolyte.
It is improbable that the effect is due merely to the change
from platinum to carbon, as there was no corresponding change
when similar experiments were performed with sulphuric acid ;
the positive charge on the hydrogen evolved being large whether
platinum or carbon terminals were used and no change occurred
by running the current for half an hour, except a gradual increase
in the charge which can be shown to be due to a rise in tempera-
ture. It was also found that the charge on the hydrogen was
increased by using a new carbon electrode, instead of that used
with the hydrochloric acid.
(29) In the case of direct electrolysis where no secondary
action takes place, or other chemical effects at the electrode, con-
siderations of polarization would lead us to expect that gases
would come off carrying with them a charge of the same sign, as
that which they carry in the electrolyte. Thus in the case of
polarization due to a layer of hydrogen with a positive charge
surrounding the electrode it is conceivable that, when the evolu-
tion of hydrogen takes place, some of the gas composing this layer
would come off without losing its charge.
(30) In seeking to explain the changes of sign that occur, as
in the case of the hydrogen evolved from hydrochloric acid, it must
be remembered that, once the gas has acquired a charge, only a
small quantity of electricity is lost by bubbling through liquids, so
that causes which influence the sign of the charge should most
naturally be sought for at the place where the gas is being
evolved, and may be due to the state of the electrode or to
impurities in the electrolyte in the immediate vicinity of the
electrode.
(31) There are some well known phenomena which point to
an explanation of the results obtained with hydrochloric acid,
namely: the electrification of gases by glowing metals*. The
typical effects of this kind are, the positive electrification of
* J. J. Thomson, Phil. Mag., Dec. 1896.
370 Mr Townsend, Electrical Properties of [Nov. 22,
oxygen when a metal is being oxidized, and the negative electrifi-
cation of hydrogen when blown past a hot oxidized metal; the
metal in the former case uniting more readily with the negative
oxygen atoms, and the oxygen in the latter uniting more readily
with the positive hydrogen atoms. The only necessity for the
high temperature of the metal is to break up some of the
molecules of the gas into atoms, but in the cases we are dealing
with the gases, at the electrode, are already in the atomic state.
We should therefore expect somewhat similar effects to take place
when the gases which are evolved can form chemical compounds
with the electrode, or with bodies either dissolved in it, or in its
immediate vicinity.
(32) If the above principles are applied to the case of hydro-
chloric acid we should expect, when the gases are evolved by
electrolysis, that the hydrogen would carry a positive charge, and
the chlorine a negative charge. The subsequent change from
positive to negative, in the case of the hydrogen, can be explained
by supposing a small quantity of hydrochloric acid to be formed
at the negative electrode, due to the action of the nascent
hydrogen on the chlorine, and that the positive hydrogen atom is
more active in forming a compound with chlorine than the nega-
tive. A similar explanation would apply to the change which
occurs from negative to positive in the charge carried by the
chlorine when platinum is used instead of carbon for an electrode,
since a chloride of platinum is formed.
(33) The charged hydrogen given off from a platinum elec-
trode, in the electrolysis of hydrochloric acid, has the same
property of forming a cloud when bubbled through water as the
highly charged gases obtained by other methods. The chlorine
- however has only a small charge, and moreover contains a quantity
of hydrochloric acid vapour which would be difficult to remove,
without making the charge too small to form a visible cloud.
The hydrogen was treated in the following manner, in order to
get rid of the acid vapour which would form a cloud when bubbled
through water. The delivery tube from the cell was connected to
the tube 7, which dipped into a strong solution of caustic potash
contained in a flask H,, and the gas then passed along a tube
containing glass wool soaked in caustic potash before it bubbled
through the water in a flask H,. The hydrogen which was
evolved from the platinum electrode, after passing through this
apparatus, was led into an insulated inductor connected to the
electrometer and, with 10 ampéres through the electrolyte, the
spot of light on the electrometer scale was deflected 37 divisions
per minute, and with 14 ampéres, 62 divisions per minute, the
1897.] Newly Prepared Gases. 371
temperature of the cell being 36°. In both cases a dense cloud
was observed above the water in H,.
In order to test the efficiency of the apparatus, for removing
the acid vapour, and at the same time to show that newly pre-
pared hydrogen does not form a visible cloud unless it has a
considerable charge, the gas evolved from the carbon electrode
was led into H,. It was found that the electrometer was giving
only 3 divisions per minute and no cloud could be seen over the
surface of the water in H,, although the temperature of the cell,
and current through it, were the same, as when 37 divisions
per minute were obtained by using a platinum electrode. In
weighing experiments were performed in order to find the ratio
of the weight of the cloud to the charge, but it could easily be
seen that the cloud was less dense than that which would be
formed in similarly electrified gas evolved from a sulphuric acid
electrolyte.
In addition to the above experiments, the effect of Rontgen
rays in discharging the gas has been examined. It is hoped that
the results of this investigation, and the experiments on con-
ductivity alluded to in section 13, will be ready for publication in
the near future.
In conclusion I desire to express my thanks to Professor
Thomson for the valuable assistance his suggestions have afforded.
(3) Ona chemical effect produced by the impact of kathode
rays. By Professor J. J. THoMSoN and Mr S. SKINNER.
Aluminium is rapidly evaporated from the kathode by an
electric discharge in a highly exhausted vacuum tube in which
air has been replaced by mercury vapour. ‘he metal is con-
densed over the walls of the tube in the form of a bright mirror.
An iron kathode gives a similar mirror in a mercury vapour
discharge tube. When the aluminium coating is dissolved off
the wall of the bulb by hydrochloric acid a gelatinous membrane
remains which gives the reactions of silica, and the escaping
hydrogen has an unpleasant odour from the small quantity of
silicon hydride which it contains. The iron mirror dissolves
completely in hydrochloric acid. From these observations it
appears that aluminium driven off from a kathode by an electric
discharge acts on the glass, forming a silicide, which on solution
in hydrochloric acid yields aluminium chloride, gelatinous silica
and some silicon hydride.
When potassium vapour is used in the place of mercury the
glass opposite the aluminium kathode is roughened. In parts
sheltered by screens from the discharge the glass is not attacked.
VOUAEX. PT. VII, 30
372 Prof. Thomson & Mr Skinner, On chemical effect, etc. [Nov. 22,
In potassium vapour the aluminium kathode is not evaporated
to any marked degree. In this case the action on the glass may
be attributed to the potassium which under the action of the
discharge attacks the glass forming soluble potassium silicate ;
so when the bulb is washed out with water and dried a frosted
surface is left.
Opposite the kathode both in the mercury vapour and po-
tassium vapour bulbs a dark annular stain of the shape of the
kathode is formed. This stain resists the action of strong hot
hydrochloric acid, nitric acid, aqua regia and potash solution.
The action of hydrofluoric acid removes it apparently by dissolving
the glass. These tests indicate carbon rather than silicon, but
the quantity of the stain is too small to make certain. The stain
is also formed on screens of mica, quartz and calcite; and this
supports the view that it is carbon fractionally evaporated from
the aluminium and iron cathodes. The sheet aluminium and iron
used for kathodes was not pure.
For comparison some pieces of an old incandescent lamp which
was blackened inside with carbon, evaporated from the filament
by long use, were treated with hydrofluoric acid and examined:
microscopically. The visible effects in this case were very like
those observed when the stain was treated with the acid. The
stain in each case was apparently in a state of tension and portions
of it curled up when broken.
Monatomic gases appear to permit the evaporation of alu-
minium, as Professor Callendar has observed its evaporation in an
argon vacuum tube.
(4) On the effect of zine and other metals on a photographic
plate. By Professor J. J. THOMSON.
In the course of a discussion at the Cavendish Physical Society
on Dr Russell’s paper on the photographic effect produced by
certain metals, Sir George Stokes suggested that possibly light
might be thrown on the question as to whether these effects were
due to radiation or to the vapour of the metals, if photographs
were taken with a stream of air flowing between the metal and
the photographic plate. In consequence of this suggestion a series
of the photographs made by zinc and amalgamated zinc (1) with
nothing but air between the zine and the photographic plate,
(2) when the zine was covered with a film of celluloid, were taken
both with and without an air blast. The photographs with the
air blast were found in both cases to be distorted, which is in
favour of the view that the effects on the photographic plates are
due to the vapour of the metals, .
1897.] Mr Perkins, Notes on some Hawaiian Insects. 373
Monday, 6 December, 1897.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
The following were elected Fellows of the Society :
Mr A. S. Ramsay, M.A., Fellow of Magdalene College; Mr
W. M. Fetcher, B.A., Fellow of Trinity College.
The following were elected Associates of the Society :
Mr J. Zeleny, Mr H. A. Wilson, Mr G. H. Shakespeare, Advanced
Students of Trinity College; Mr J. H. Vincent, Advanced Student
of St John’s College; Mr P. Langevin, Advanced Student.
The following Communications were made to the Society :
(1) Notes on some Hawanan Insects. By R. C. L. PERKINS.
Amongst the most important representatives of the Order of
Neuroptera in the Hawaiian Islands, are the dragon-flies of the
genus Agrion. Several species are found on all the more import-
ant islands of the group, and the range of many of them extends
over several islands; wherein they ditfer from the greater part of
the endemic insects, which are for the most part confined to a
single island; or to one or two of those which le most closely
together. At the same time, when a series of examples of a
species from different islands is compared, certain more or less
constant differences are often ‘observable, especially as regards
size.
But the most interesting facts relate to the earlier stages or
nymphs, which are aquatic and carnivorous. Excluding these
dragon-flies and a few water-beetles, the insect fauna of the
streams and pools is almost non-existent. The Ephemeridae,
Perlidae, and Trichoptera, usually so numerous, are entirely un-
represented in the Islands, although the mountain streams, rising
at high altitudes, with their superb waterfalls, and various
temperatures, appear admirably adapted for many of these. It is
therefore not a little surprising to find the group of dragon-flies so
well represented, and that the individuals are so numerous, being
on the whole the most conspicuous of all the endemic insects. In
the absence of the groups above mentioned, I believe that their
main food-supply comes from without, consisting of such creatures
as accidentally fall into the water. Under ordinary circumstances
this is not great, but after rain, when the streams rise very
quickly, food becomes abundant. When the streams, as is often
the case, become nearly dry, large numbers of creatures resort to
374 Mr Perkins, Notes on some Hawaiian Insects. [Dec. 6,
the pools that are left, for the sake of the moisture, and the
numbers that come to grief is often astonishing, the whole surface
being covered with the drowned and drowning.
There are, however, other species the nymphs of which live
under very different circumstances. These have given up their
aquatic life, and live hidden at the bases of the leaves of a
liliaceous plant—Astelia veratroides. Sometimes a little water
is held by the plant around the stem, but more often there is
merely a collection of damp earth and dead leaves. These nymphs
would even appear to dislike the collections of water, for in wet
weather they often crawl halfway up the leaves, instead of
remaining at the base, where the water accumulates. They differ
in some points from those which frequent the water; they are
shorter and stouter, and much more sluggish, and the caudal
appendages are very short and thick, differmg therein greatly
from some of the aquatic species, the appendages of which form
beautiful tracheal gills.
On the whole they are without doubt better off as regards
a food supply than the aquatic species, for there is generally
abundance of animal life around them. A number of interesting
beetles breed only in this plant, and minute young of molluscs
and earthworms are generally abundant in the same, as well as
the larvae of small moths. Moreover nymphs of various sizes
often frequent a single plant, and if hard pressed for food the
larger, no doubt, devour the smaller individuals.
In consequence of these habits, some of these species of dragon-
flies, although their powers of flight are feeble, may often be seen
in numbers in localities remote from water, and where they would
not naturally be looked for.
These terrestrial nymphs are able to endure extreme drought.
On one occasion when out shooting, having no more convenient re-
ceptacle, I carried a number for the greater part of the day in an
envelope. In the evening, although very dry, they were still quite
lively. They were then placed in a tumbler of water, where they
remained on the bottom, not being able to crawl up the sides.
Here they remained for a day, apparently as happily as on dry land,
when they were taken out and preserved.
To turn to the Order of Coleoptera, which is more richly
represented in the Islands than any other, by far the most
conspicuous are the species of the genus Plagithmysus. With
the allied genera Callithmysus and Clytarlus they form a special _
group of Longicorns, and no nearly allied form is known from
elsewhere. Hence the country from which they may have been
derived is quite uncertain. About 40 species are at present
known. These beetles are remarkable in many ways, more
particularly for the manner in which the wings are folded, there
1897.] Mr Perkins, Notes on some Hawaiian Insects. 375
being no transverse folding, so that they project beyond the elytra;
secondly in the small development of the hind-body, at least
in the males; and thirdly as being furnished with three distinct
sets of stridulating organs. With regard to the latter the thoracic
arrangement for stridulation is of the usual kind. The second
mode by which sounds are produced, is by rubbing the bases of
the hind femora against the margins of the elytra. These margins
are specially sculptured much like a file, and the parts which rub
them are roughened with minute tubercles. Altogether the
arrangement reminds one not a little of the stridulating organs
of the grasshoppers, and the Plagithmysi themselves have some
little resemblance in general appearance to those insects. The
third set of stridulating organs, which were discovered and
pointed out to me by Dr Sharp, are on the basal joint or coxae of
the middle and hind legs, and they may really be considered as
two distinct sets, since the middle pair operate on the adjoining
edge of the thorax, the hinder pair on a ridge on the basal segment
of the abdomen. Moreover, in a specimen of P. aequalis
examined, the striation of the coxae on either pair of legs was
different, being evidently coarser on the intermediate pair.
It is highly probable therefore that by the use of these different
organs a considerable variety of sounds can be produced, for the
sound made by the legs when rubbing against the elytra is not
the same as that produced by the prothorax rubbing on the
scutellum, and the degree of pressure, or rapidity of movement,
also causes a variation in the sounds. The insects run with
extreme rapidity over the tree trunks, when the sun shines hotly
on them, and often perform curious evolutions, running in short
curves or zigzags and at times almost giving little leaps. It seems
_ hardly possible that such movements can be made without stridu-
lation, although the sounds are not audible unless the creature is
held in the hand.
The small size of the hind-body may be connected with the
frequent great disparity of size between the sexes, for the females
of many of the species are often relatively very minute, and
probably in all the species many such individuals would be found
were sufficient material available for examination. While the
minute males are not affected by the almost rudimentary condition
of the hind-body, were this of the usual length, many of the
large males would be quite unable to pair with a large proportion
of the females. As it is, this is not the case, and male and female
will often pair though the former is several times the bulk of the
latter. Moreover it should be mentioned that both sexes are
polygamous and pair many times. It is possible however that the
rudimentary condition of the hind-body is in some way connected
with the stridulating organs.
376 Mr Perkins, Notes on some Hawaiian Insects. [Dec. 6,
The extreme variation in size of a given species may be due to
differences in the quality of the food of the larvae, which may
be found in a tree which has only just fallen, or begun to die,
while others are feeding on a tree the wood of which is in a much
drier condition.
One of the most interesting points in regard to the Plagi-
thmysi is the extreme variability of most of the species, which
affects not only the colour but also the structure. The variation
in the latter, however, is not so readily appreciated as the colour-.
variations, and I do not propose to refer further to it here.
Variation in colour is shown in various parts of the insect but is
more especially remarkable on the posterior femora.
On the Island of Hawai there are four very closely allied
species of the genus. Three of these, P. varians, darwinianus, and
lamarckianus, are found in the same locality, but each is solely
attached to the kind of tree on which its larva feeds. Where the
different trees grow side by side the three Plagithmysi may be
found side by side; but in some parts of the forest only one of the
three trees is to be found, in which case only the one species
whose larva feeds on it is also found. The fourth species, P. black-
burnt, feeds on the same tree as darwinianus, but occurs on the
other side of the island.
All of these species are variable in the colour of the femora,
but the variation as exhibited in a series is distinct in each. In
some cases the variation is so great that the extreme forms would
appear to be more distinct, than are some of the allied species
from each other. I have examined a considerable number of
individuals of each of these species which are here exhibited.
Thus of P. darwinianus, which feeds on Sophora chrysophylla,
an acacia, the 65 individuals all have the femora red, the apices
being very rarely dark.
Of P. blackburni which feeds on the same tree but not in the
same locality, 68 have these parts black, only 5 red.
Of P. varians, which feeds on Acacia koa, 41 have the femora
black, 53 have the apices bright red, while 4 are nearly entirely
of a reddish colour.
Of P. lamarckianus, which feeds on trees belonging to the
Urticaceze, the legs are wholly black or reddish, probably either
variety being about equally numerous, the species being much less
common than any of the preceding.
Thus on the whole each species divides into two or three
varieties without true intermediate forms. It is true that if some
of the individuals of P. varians be closely examined, the apices of
the femora are seen to be less dark (ie. slightly reddish), but
these fall in naturally with the black-legged specimens, and are
very far removed from the brightly coloured examples.
1897.] Mr Perkins, Notes on some Hawaiian Insects. BY a |
The only other species examined is P. aequalis, a species very
distinct from any of the preceding, found on the Island of Kauai.
The variation in this species is similar in kind to that of P. black-
burnt, but the relative numbers of each variety are very different,
for while in that species the red-legged variety is extremely rare,
in the present one out of 181 examined no less than 70 are of this
form. The large amount of variation exhibited is the more
remarkable on account of the limited distribution of the species,
for not one of the genus is known to inhabit more than one
island, and many of them are certainly confined to a very small
area of the island on which they are found.
It has been already mentioned that all the species are polyga-
mous. Of selective pairing by the different varieties there is no
trace. On one occasion when watching a number of P. varvans
on a fallen tree trunk, I noted that a female of the black-legged
form paired successively with the brightly coloured variety, which
has the apices of the femora red, then with one of her own
colour, and shortly afterwards with the extremely rare variety
which has the legs entirely dull red—And instances of a similar
kind can be noticed any day, where a species is plentiful. Were
sexual selection operative there is no doubt that a much larger
number of distinct forms would be produced. It is interesting to
consider the conditions that have brought about the specific dis-
tinctions in these species so closely allied. Taking into considera-
tion the fact that no species is found on more than one island,
either geographical isolation, or a difference in food, or a combina-
tion of these two factors, seems to account sufficiently for the
separation of the species. Of the species under consideration,
three may be found side by side (although each of them is also
found in places apart from the other two), yet each keeps entirely
to the tree on which its larva feeds; and the other P. blackburni,
although it has the same food as P. darwinianus, does not inhabit
the same area.
So far as the native fauna is concerned these Plagithmysi
have few enemies. It is doubtful whether any parasites attack
them ; if any do so, they are certainly of extreme rarity. Except
on the Island of Maui, birds either leave them alone or perhaps
are very rarely able to catch them. On that island, however, one
of the Drepanididae—Pseudonestor—is extraordinarily modified in
accordance with its habit of living on the larvae, pupae and
immature beetles of this genus and the allied Clytarlus. Indeed
its food consists chiefly of these creatures, which it is able to tear
out from the hardest wood. The great scars, made on trees which
are affected by the beetles, may often be seen as the result of the
work of this bird, and when opened its stomach is usually filled
with their larvae.
378 Mr Perkins, Notes on some Hawarian Insects. [Dee. 6,
Like the other orders of Insects the Hymenoptera are repre-
sented by a very few types out of the enormous number that exist
elsewhere. ‘Thus the bees, excluding a few isolated forms, which
have either certainly or probably been introduced by man, are
represented by a single genus; the wasps also by a single genus,
and the Fossors by two genera of Crabronidae, and two closely
allied forms of Mimesidae. It is to the remarkable evolution of
species of each of these types that the comparative wealth of the
aculeate hymenoptera is due. Thus while there are a very few
genera which can be looked upon as endemic, the average number
of species to each genus is very great, this number being about 28.
Most numerous of all in species is the genus Odynerus represented
in the Islands by some 80 distinct forms. They are one of the most
important elements in the fauna, and are sufficiently numerous to
attract the attention of people not particularly interested in such
things, the more so as one or two of the species abound around
houses, and avail themselves of holes in woodwork or furniture
for forming their cells. Although intimately related to one
another, and extremely similar in general appearance, in reality
they exhibit a very great variety of structure. If one collects
these wasps over the Islands from Oahu to Hawaii, the general
blackness of their colour is very remarkable. Some are more or
less marked with red, the markings being rarely noticeable, unless
the insect is caught and examined, and a few have one or two
narrow bands of a pale yellow colour on the hind-body, which
also are not as a rule easily noticed. Many are entirely black.
If now one compares with these a collection of the species from
the Island of Kauai a difference is at once seen. Excluding one
or two species which frequent the coast and, scarcely modified,
have a wide distribution over the Islands, all the species have two
distinct yellowish abdominal bands, the second being nearly always
evidently wider than the first. When the insects are on the
wing, these bands are plainly seen. It so happened that im the
course of my collecting over the Islands, Kauai was not visited
until after the other islands had been collected over, so that it
was no small surprise to find the wasps so distinct in superficial
appearance. At the time I supposed that the Kauai species would
turn out to be very closely related to one another, at least more
closely than to those on the windward islands. This however
proves not to be the case, for some of the most remotely allied
species on the other islands, are represented on Kauai by species
which are structurally only slightly modified forms of the same,
although their superficial appearance is very distinct. For some
reason or other it is clear that the Odyneri of Kauai have assumed
an appearance almost unique amongst the great number of species
occurring in the Islands—they have what are called ‘warning
1897.] Mr Perkins, Notes on some Hawanan Insects. 379
colours’. That these markings have any such significance is I
think certainly not the case. There is no reason to suppose that
the species on Kauai have any more need of their special
coloration than the black species of Hawaii, but rather the
reverse, as birds, which are their only possible enemies, are more
numerous on the latter island. As a matter of fact, after the
examination of the food of many individuals of nearly all the
endemic birds, I have never found them to feed on any of these
insects whether black or coloured, nor would the majority of them
be the least likely to do so, on account of their habits and
structure. For the most remarkable feature exhibited by the
endemic land-birds is the specialization of form for the purpose of
securing some special food, which has led to the extreme diversity
of structure exhibited in a group so small as the Drepanididae.
So extreme is this specialization of some of the birds, that their
food is almost limited to one special form of plant or animal, as
we have already seen in the case of Pseudonestor,; while even in
less specialized birds the range of food is very small. It is just these
most highly specialized birds that are the first to disappear when
their natural surroundings are interfered with, as they have already
done on the Island of Oahu, which has been more upset than the
rest of the group, by foreign settlers. It is not exaggerating to
say that the extinction of a few species of beetles would extermi-
nate both Pseudonestor, and the various species of Heterorhynchus,
while the disappearance of three species of trees would do the
same for the three genera Rhodacanthis, Chloridops, and Lox-
ioides, and many of the other birds are equally dependent on a
particular section of either fauna or flora.
The birds most lkely to feed on the Odyneri are the fly-
catchers of the genus Chasiempis, which do not appear to do so,
but confine their attention for the most part to small Lepidoptera
and their larvae. If they did feed on these, one would expect the
Odyneri of Hawai to have distinctive marks as well as those of
Kauai, since the birds are equally common upon both. But there
is every reason to believe that the colours of the insects have no
such significance, and it is still further convincing to notice that
the Odyneri of Molokai have a general tendency to red-markings—
Molokai being an island where no fly-catchers exist,—while on
Hawaii these insects, even in certain points of structure of
secondary value, tend to greatly resemble each other.
The distinct style of coloration of the Kauai species is a point
of some importance, for it has long been known that in other
- countries insects of this group have a great general resemblance
to one another in the country they inhabit, as for instance the
highly endemic species in Australia and Chili. No doubt, were
they more widely known, these cases of Chilian and Australian
WO. IDG, PaO 31
380 Mr Perkins, Notes on some Hawaiian I nsects. [Dec.6, 1897.
insects would be referred to as good instances of what are called
‘warning’ colours, but from the study of the Hawatian species
such a significance becomes very doubtful. It seems much more
probable that they are due to the general condition of the country
they inhabit—it may be climate or some such cause.
(2) Remarks on a journey to investigate the habits and develop-
ment of Lepidosiren paradoxa. By Mr J. Granam Kerr, B.A,
Christ’s College.
PROCEEDINGS
OF THE
Cambridge Philosophical Society.
Monday, 24 January, 1898.
Mr F. DARWIN, PRESIDENT, IN THE CHAIR.
The following communications were made to the Society :—
(1) A New Method in Combinatory Analysis with applica-
tions to Latin Squares and associated questions. By Major P. A.
MacManon, R.A., Se.D., F.R.S.
This paper is printed in the Transactions, Vol. xvi. Part iv.
(2) Abelian Functions in connexion with two-dimensional
fluid motions. By H. F. Baker, St John’s College.
1. Consider the portion of the upper half plane of the complex
variable ¢ which lies outside p circles, which do not intersect each
other or the real axis. Then the function which gives the streaming
motion in this portion of the upper half plane due to a doublet of
arbitrary strength and position is already known (Joc. cit. (8), (@))*.
* The references given to the literature are by the Greek letters, as follows:
(a) Riemann, Ges. Werke (1876), No. xxy., p. 413 (or second edition, p. 440); (8)
Schottky, Crelle, lxxxiii. (1877) ; (vy) Schottky, Crelle, ci. (1887) ; (6) Schottky, Crelle,
evi. (1890); (0) Burnside, Proc. Lond. Math. Soc. xxii., xxiii., and Messenger of
Mathematics, xx. (1891); (x) the writer’s Abelian Functions (1897), Chap. xii. ;
(A) Kluyver, Acta Math. xxi. (1897).
VOL. IX. PT. VIII. oe
382 Mr Baker, On Abelian Functions in connexion [Jan. 24,
As we shall require the result, and to illustrate the pomt of view,
we give a proof.
Denote the real axis by C,; the points of the circles which are
nearest to the real axis by Cy’, ..., C,’, and these circles themselves
by the same letters, reckoning from right to left ; denote the region
bounded by (, Cy’,... , Cp’ by Q); denote the circles which are
the images of C,’,..., C,’ in the real axis by C;,..., Cp, the points
of them which are nearest to the real axis being also denoted by
C,,..., Gy; denote the region bounded by the 2p circles Cy’, ..., Cp,
C,, ..., Cy by Q, the axis C, being then disregarded. Then it is
known (loc. cit. (8)) that there exists a function, G, single valued
in 0, save for real periods, real on O), Cy’, ... , C,’, and infinite at
an arbitrary point €=¢ like (P+7Q)/(€—t), where P, Q are arbitrary
real constants. Being real on (, this function will (Schwarz, Ges.
Abh., 11. p. 66), have the same value at any point of the caircum-
ference C, as at the point of the circumference C,’ which is its
image in C,, and will be infinite in Q, beside at ¢, at €=#', where
t’ is the conjugate complex of ¢, namely like (P—7Q)/(¢—?¢). Now
the region © when considered as the locus for functions whose
values at any point of one of the boundaries Cy’, ... , C,’ are equal -
to the values at the conjugate complex point of the boundaries
O,,..., Cp, is a p-ply connected Riemann surface, for which the
fundamental functions are well known (loc. cit. (x)). It follows
therefore from the theory of functions on such a surface that for
proper values of the constants A,, ..., 4p, A, the function desired
is given by
@=—(P+iQ)T?*—-(P- iQ) Te" + Awe? +... + Awe + A;
here A is an arbitrary real constant, and A,,..., A, are determined
by
Ayti» +... + Aptp,r = 270 [(P + 1Q) ob, (2) + (P — 20) 6, (DI),
(7 = 1a 5 ee
where ¢,,() denotes dv"/dé ; the point =a is supposed taken
on Ch.
By applying similar reasoning we find for the function giving
the general circulatory motion in Q,,
ON Paes $5 a $3
briny =Bor’ +... + Bu +B,
where B,, ..., By are determined by the values of W on Qj,
Cy,..., Cy’; and infer, by the way, that ye" is real when € and a
are real, and that 7,,,is a pure imaginary, so that the constants
A,, ..., Ay above are real (loc. cit. (), (X)).
3
1898. ] with two-dimensional fluid motion. 383
Therefore when €, a are real
(P +iQ) 19+ (P — iQ) Te",
is real; as can be shewn from the explicit formule.
This function is single valued in ,; it has its imaginary part
constant on each of the circumferences CY’, ..., C,’.
2. The problem of Riemann’s paper (loc. cit. (a)), in which
however the boundaries are not necessarily circular, is the deter-
mination of the solution, for the region Q,, of the potential
equation
ol Of 1? U
Of * On?
which is finite within ©, and takes on the boundary an assigned
continuously varying value wv. This is given, at t = & + in, by
U =/uP*
=),
where P%is the function real on the boundary of Q,, Nee only real
periods, which is infinite at the interior point ¢ like 5— log (€—t).
This function is known (loc. cit. (X)), or follows as rite from the
theory of a Riemann surface, being given by
1 i a
SS ple ae ake + A,v8 Al
Pi =
where ¢’ is the conjugate complex of t, a is real, A is a real constant,
A,,..., A, are real constants determined by the equations
8 4 Ayr toe + Apty,r =O, (r=1, 2,..., p).
3. Among the single valued functions for the region 0, with
rational infinities, there is one of particular interest—that namely
which is real on the boundary and has a single pole of the first
order at an assigned point of each of the (p + 1) separate boundary
curves (,, Cy,..., C,. This function effects a conformal repre-
sentation of the region ©, upon an infinite half plane (p + 1) times
covered, and is thus the direct generalisation of the function giving
the conformal representation of a simply connected region upon a
simple half plane.
In what follows we put down this function for the case when
the circles .C/’, ..., C,’ are unrestricted (save by the inequalities
which are necessary for the convergence of the series involved);
and then give the very simple form taken by the function when
the Abelian functions involved are those of hyperelliptic character.
32—2
384 Mr Baker, On Abelian Functions in connexion (Jan. 24,
The construction of a function, single valued in the region
Q, unchanged by the substitutions which transform the circles
CY’,..., Cy respectively into C,, ..., Cp, and having p +1 poles of
the first order within Q, of arbitrary position, is known—being as
follows (loc. cit. («)); let the poles be at z, q, ... , cp, and let
ae (Yr2 + 8)? :
@ (Zz, ee Bo le ?
let the additive arbitrary constant be determined by the condition
that the function vanishes at =a; then, the function is given by
1G | WE, Oy Oy a) GiB Gh), sea OE Gs) |;
OG, 6) O(GsQs DGsGh sa, OG, Gs)
OE 56) QEGy@y OGpah) a5 OGa Gs)
ey. iP I Na React i
where # is an arbitrary constant, and a, ... , @, are the analogues
of a by the p fundamental substitutions whereby the circles
Cy, ..., Cy’ are respectively transformed into C),..., Cp. In the
case under consideration the region © has the specialty that the
circles Ci, ..., Cp are the inverses of C,’, ..., C, in regard to (,>—
we proceed to prove that in this case, if z be upon the real axis
C,, and ¢,, ..., ¢) be respectively upon the circumferences CY’, ..., Cy,
then, for a suitable determination of the constant H, the function
is real upon each of the curves C,, Cy, ..., Cp. The necessary
value for # is that of the inverse of the minor of ®(z, f) in the
determinant (or any real multiple of this)—when # is so determined
the function may be denotod by W({, a; 2, G, ..., Cp).
To prove this it is sufficient to prove that the function is real
upon the real axis (Schwarz, Ges. Abh., IL p. 66). Now it follows
from Riemann’s theory that the function, uniform in ©, unchanged
by the p fundamental substitutions, with poles at z, q, ..., Gp,
respectively on C,, Cy’, ..., Cp’, and vanishing at €=a, is given by
P(E) = (Prt iQ) TE" +... + (Pp + 1Q)) PE" + (P+ 1Q) PES
where P,, Q,, etc., are real constants whose ratios are given by
(Pi + iQ,) bn (@) + +. + (Pp + 1Qp) dn (cp) + (P+ iQ) $n (2)=0,
@ Sse
where ¢,, (€) = dv® “[dé We have already seen that ¢, (£) is real
when € 1s real; hence these equations involve also, if c,, c, be
conjugate complexes, the equations,
(P, — 10h) dn (G)+. aa (Py oF Wp) Pn (Cp oa (P a - Pn (z) =0,
@=1) 2) Ree
2. See
1898. ] with two-dimensional fluid motion. 385
which, in turn, shew that, a being real, the function
Ai (6) = (Pi =) Ve" +... + (Pp — 1Q,) TS + (P iQ) TE
is a single valued function unaltered by the fundamental substitu-
tions. The poles of f,(¢) in the ¢ plane are however the same as
those of f (£), since ¢,’, c, are analogues of one another for the r-th
of the fundamental substitutions—and the functions /,(f), f(£)
vanish at the same place a. Wherefore, considering the residues
at the pole z, we infer
(P+ 1Q)7F(E) = (P10) AO);
as we have already shewn that for conjugate complex values of ¢
the quantities
a a ee 10) re",
have conjugate complex values, it follows that the function
(P+7Q)71 /(€) has the same property.
This proves the theorem in question.
4. The same argument can be used to establish the further
result: Take p +1 points entirely within the region Q, so situated
that those which are not upon the real axis C, consist of pairs
occupying conjugate positions in regard to this axis. The uniform
function unaltered by the p fundamental substitutions which has
these points for poles of the first order is necessarily real upon
C,, Cy, ..., Cp’ (and C,, ..., C,), or can be made so by multiplication
by a proper constant factor. For the region ©, this gives the
theorem: take any m points within ©, or upon one or more of the
circumferences Cy’, ..., C,’, and any & points upon OQ, so that
2m+k=p+1; there exists a function uniform in Q,, real on
CY, ..., CG,’, G, and infinite to the first order at each of the m+k
points taken in Q,.
It may be of interest to give the functions of §§ 3, 4 for p=1.
Let the fundamental substitution be
(De =A) (SB) (eA)
and v=|Vm|. Then if be any real quantity,
ee | Sa lou pe alo (- =
men = AG,| AC ° ae BY OO ae 8 io BS Ay?
(forms which hold when (, becomes a circle, C, being the point
where the straight line C/C, cuts the circle C,), the general and a
particular form of the function of § 3 are given by
errs Oe eae: ae) xe Ce
Q(u)—e(v) eE(u)—-—@E(Wt+e’)’ O(u)—¢e’
386 Mr Baker, On Abelian Functions in connexion [Jan. 24,
where », w are real; and the function of § 4 by
PM+EO PF WH+O'O)
E(M)—eE%) e(u)—e)”
where ¢ belongs to a point in Q,, and ¢, is the conjugate complex
quantity.
The function of § 1, which is real on C/’ and C), and has only
real periods, and has one arbitrary pole of the first order in Q,, is
given by
oye OOO ps gy CORO ple eee
COT p ote pape Te? EO —e)
where P, @ are real quantities.
5. We consider now the case in which the circles G, Cy,...C,’
are all cut at right angles by another circle O. It is known that
in this case the functions arising reduce themselves to hyper-
elliptic functions. The figure (1) drawn for p =3, will explain the
notation we adopt.
In any case where the 2p circles C,’, C,, ..., C,’, Cp consist of
pairs of circles inverse to one another in regard to the real axis Cj,
1898.] with two-dimensional fluid motion. 387
the singular points lie within the circles CY’, O,, ..., O,', Cp, and
consist of pairs of points inverse to one another in regard to O).
This is clear either because the substitution 5, is equivalent to an
inversion in regard to the circle C, followed by an inversion in
regard to the circle C;,, or, what is the same thing, by remarking
that if
P=. 9O9 PHM.
be two substitutions in which the primary factors occur in the
same order but are the inverses of one another, and, if z, 2’ be
conjugate complexes, then also ¢(z) and ¢’(2) are conjugate
complexes. But in the case in which the circles Cy, C’, ..., Cp’ are
all cut at right angles by another circle, O, it follows further that
the singular points all le upon this circle O.
Hence follows immediately another consequence; we have
already seen that the imaginary part of the function
o ii > log So siCBn)
275° §—34 (An)
is constant on each of the circles Cy’, ..., C,’, C), being zero on C;
it can now be seen that the real part of v$ is constant on each of
the arcs of the orthogonal circle O which are limited by the circles
CY,...,Cp,C,,..., Cp. For ifj, 7’ denote two substitutions such as
¢@ and ¢’, we can put
1 6-9) (Bn) €-3) (By)
$ —— > ] = Ra ATE i = 7 >
On 20 i,j °8 o— ae (An) c ae aj (An)
and 3; (Bn), 3; (An)—as also $j (Bn), 3; (An)—will be two singular
points having conjugate complex positions upon 0. As the real
part of v§ depends only on the arguments of the factors
[S—3) (Bn)I/[E— Sy (An)],
the result follows at once.
ys
n
From this, if barriers be drawn in Q, consisting of the p straight
lines joining CC, C,C,,...., Cp Cp, we find the equations
yin Go = —4, or 0, as N=7, Or N=7.
It will be sufficient to consider one case. Let D,’ be the inverse
point of C,’ in regard to the circle O, and let A denote the real
part of v%% at the point a,; then since the function — 1 is real
on the are ac, it has conjugate complex values along the ares ¢,Cy’,
c,D,/; so that we have on these arcs, respectively,
= aoe Ja
ots i a 08% = — $y, 1— My
388 Mr Baker, On Abelian Functions in connexion [Jan. 24,
where yp is a variable real quantity; again, since —7(v2%— K) is
real on the are a@,¢,, it has conjugate complex values on the arcs
a,C,’, a,D,{; so that we have on these ares respectively
ve ?= K— 37, +X, ve4= K —$7,,—2,
where p is a variable real quantity ; therefore
Oe ce; — uD Cy + Ope D,! —— vr C= Oe Cy,
while, on the other hand,
OD cu Oe 4 I + Ub» CY
where II represents the value obtained in passing from one side to
the other of the barrier through CY, =—1 when r=1 and =0
when 7+ 1, it being supposed that, as in the figure, the arc cq 1s
in the counter-clockwise direction ; hence we have by addition
Zu % = TT,
giving the result enunciated. This equation is also easily seen to
be the condition that the function v%“% be continuous at Dy’.
For these results ef. Joc. cit. (@); the proof here given is de-
signed to bring out the identity with some corresponding results
in the theory of a hyper-elliptic Riemann surface; it is upon this
identity that an important result deduced below is made to rely.
Further, since the real part of v$ is constant upon the separate
arcs of the circle O we obtain
Oy @ — il by Oh a IL 1
CBee > ony ae IS St a OHA, OP
Cx) Oh, —> A AL, GO; Gy — al.
OS 2= OTr, Oana OTr, 3) UR 7= OTr, 3>
of which for instance the value of v%% can be obtained by a
method similar to that employed above, by adding the values
obtained by passing from a, to ¢,, first directly along the circle O,
and then along the path a,0{'C,a)'c,'0,C,'c,, where a, ¢, are the
images of a,, c, on the circle C).
These equations shew that, for the definition of the half
periods, the points a, ¢, G1, C:, M2, ..., are exactly analogous to
the branch places denoted by the same letters when the period
loops of the hyperelliptic Riemann surface are drawn as in the
annexed figure (2).
Hence from the theory of hyperelliptic theta functions we infer
that the theta functions © (v% %), O (vs °) vanish respectively in the
FOUKEAS (Cin ace GY) BACH (Giz ooo5 Ga))
1898. ] with two-dimensional fluid motion. 389
Consider now the function
?
ne yak HERI?
(f ) Si TST,
where ¢,=(a,€+B;)/(y,€+6,), and the summation extends to
every substitution of the group. When one of the p fundamental
substitutions of the group, as given by the positions of the circles
on the ¢ plane, is put into the form ¢°=(af+ )/(yf+ 8), with
aS — By =1, there is an ambiguity as to the signs of the quantities
a, 8, y, 6, which must be settled beforehand in order that the
Fig 2.
function .(¢, w) may be definite. There are then 2” functions
r(¢, w), differing according to the conventions adopted in the case
of the p fundamental substitutions. It is known (Camb. Phil.
Proceedings, Vitt (1895), p. 332, or loc. cit. (x), p. 8368) that any one
of these functions has, in the region Q, beside €=%, p zeros
}41, +++, &p Which are given by the equations
aw mot we “P= 4 (Gr oi hy), (r =1,..., Pp),
where m,, ..., m, are the zeros of the theta function © (v>™), and
(fi +h), «+> (Gp + hp)
is an aggregate of p integers, each of which may be taken to be
either even or odd according to the conventions, explained above,
adopted for the signs of a, 8, y, 6 in the p fundamental sub-
stitutions.
Hence we deduce, if the conventions be taken so that each of
Gr +h, is an even integer, the functions
r(E a), r(G ¢)
vanish respectively in (dy, ..., dp) and (c, .... Cp»). More generally,
from the results developed above, such as v,“” “= — 4, we have, the
390 Mr Baker, On Abelian Functions in conneaion [Jan. 24,
p finite zeros of any one of the 2” functions X (€, a) are (fy, «--, Mp),
where 1, 1s either a, or c,, according to the convention adopted for
the signs of a, 8, y, 6 in the p fundamental substitutions. A direct
verification is given below.
Therefore, from what was proved in the general case, a function
which is uniform in the region O, unaltered by the substitutions of
the group, real on the circles Cy, Cy, ..., G,, Cy, ..., Cy, and in-
finite to the first order on each of these circles, is given by
Z=2(E, a)/r(E, ¢);
with the notations explained loc. cit. («), save that c, replaces b,,
this can be put into the various forms following, where pm is an
arbitrary place,-and a constant factor is disregarded,
= 6) (v% ®) ell” Bw
)) (us 3) C, a)
_a(G0)a (bm)... #6 4)
oS OYa(G G)) doo @ (SG) ©
Oe [v— ax (a,)| ... [ec —2(a,)]
aX x(a—a«2(G)]... [e—x(c,)]
In the elliptic case, with
= pom Pane? fe nina
a, € NH, Cy ap, Cp?
Z
ins We Oe log (
dtr
€¢-B j;a-B )
c—A | a—A/’
we have, with the convention of sign here adopted, save for a
constant factor,
x(Ea)_ Ve@—e _ gt)
M50) Ve(uta)—e 9(u)— es’
the points c,, a, c, a@ corresponding to the values @;, @, &, © of
Q (wu), respectively. It is easy to verify that this function has the
desired behaviour.
Thus by the function (6 'a)/X(E c) the conformal repre-
sentation required in Riemann’s paper referred to, is effected.
6. We explain now how to obtain a direct verification from
the series itself of the statements that have been made as to the
zeros of the function X (fa). For this purpose we suppose the
circle O, which cuts the circles (, Cy, ..., Cp at right angles, to
be the axis of imaginary quantities, the point a being the origin,
¢=0, and the left side of the imaginary axis being the interior of
the circle O. Then we may put
SSO, Ch SUir, CG Silin, C= dey on-
2
- ——
1898.] with two-dimensional fluid motion. 391
where k,, h,, ky, ho, ... are real positive quantities in ascending
order of magnitude. It is then found that, for positive integral n,
we have
% aMe+ BO SE —h ky”
are) = ar) NG) a yi? Sir
where a6" — By” = 1, and
() os (oe ag my “3 (ee = ey
Ohl, Why — Vie) Wiig + Vd S
mace ce)
Vh, —Vk Vh,y + Vk;
the square roots Vh,, Vk, k, being taken positively; here e,, = +1, is
a quantity which is not determined by the positions of the circles,
but must be assigned when the substitution 3, is put into the
form
i (gj== ae
ye 8
with a6 — BMy” =1,
From these it immediately follows that if z be a pure imaginary
quantity, and 2 =—z be its conjugate complex, y,’2+ 6,” 1s real
and equal to yz’ + 6”, while ay 2 + 8)” is purely imaginary and
equal to the negative of al") 2! + B", Therefore if
=e 21 Q No len eye)
o (=. WIP. OTS,
/ —ny Ta a af+f8 Ei fet
FO ee
be two substitutions in which the factors formed from the primary
substitutions follow one another in the same order, but for pty
factor SY? in the first there enters, in the second, the factor Sz”
follows, if z and 2’, =—4z, are conjugate complex quantities, ae
$ (z)=— $' (2), and yz+ d= 9/'2'4+06. These facts are clear
enough from a consideration of the figure. For our purpose
another fact is also necessary, namely
when ¢,=-+ 1, we obtain
ac.+ 8 =—¢c,=¢,/, y%c,+80 =1,
when ¢,=—1, we obtain
aa, +B" =—a,=a,, ya,+6% =
where ¢,, a, denote the conjugate ae of ‘c, and a, ‘re-
spectively.
392 Mr Baker, On Abelian Functions, &c. [Jan. 24,
Hence, retaining the notation for ¢ (£), ’ (6), if
8%. O= Grp
so that
AL+ Baad [aries BM] +8 [ye+ 8)
we have
when ¢, = 1, Ac,+ B=a'c,’ + B’ =— (ac, + B),
when ¢,=— 1, Aa,+B=da, + B =—(aa,+ 8);
we find also, in fact, in these two cases,
$ (Cr) =— P'S; (Cr), & (Gr) = — $'Sy (Gy).
Thus it follows, that when e, = 1, the series
GEOn) 1
ME O= si YE + Om) aye ee
(0) m Cm mms + Bm
vanishes for €=c,; for when €=c, the term arising by the
substitution $, of the group, is equal and opposite to the term
arising by the substitution ¢’$,. Similarly when ¢,=—1, the
series vanishes for =a,.
In a somewhat artificial way this result may be included in
the statement—the series, \ (§ a), has, beside = 0, the p zeros
Ata A, — Cy Up + Cn _ An — Cy
5 Oe 5 eae eae
where €, ..., €, each equal to +1, are the signs determining the
p fundamental substitutions, as given by putting n=1 in the
formulze written down above for the substitution S$”.
(3) On the production of a cloud by the action of ultra-violet
light on moist air. By Mr C. T. R. Witson, Clerk Maxwell
Student.
If the light from an arc lamp be brought to a focus, by means
of a quartz lens, within a vessel containing moist dust-free air, a
bluish fog becomes visible in the course of a few minutes along
the path of the light. The cloud particles remain in suspension
for hours after the light has been cut off. The phenomenon is
shewn even in unsaturated air, but the faint blue haze which
then developes takes much longer to form. When the radiation
is not sufficiently intense to shew these effects a dense fog can
still be obtained by bringing about slight supersaturation by
expansion. These clouds, unlike those obtained by Tyndall (Phil.
1898.] Mr Wilson, On the production of a cloud, ke. 393
Trans., 160, p. 333, 1870) and by Aitken (EZdin. Trans., 39, 1.
p. 15, 1897) by the action of light on various vapours, are due to
the ultra-violet rays alone; for if a thin sheet of glass or mica
(substances which are opaque to these rays) be interposed, not a
trace of fog or rain is formed even when a high degree of super-
saturation is brought about by expansion. It is possible that the
small particles to which the blue of the sky is due are the result
of this action of the ultra-violet rays, of which sunlight, when it
first enters our atmosphere, doubtless contains a plentiful supply.
(4) On the use of logarithmic coordinates in Physics. By
Mr J. H. VINCENT.
(5) On the Dine Reflection of Rontgen Rays. By J. J.
THomson, M.A., F.R.S
It is well known that when Réntgen rays fall on a solid or
liquid surface there is a diffuse return of rays from the surface ;
these diffusely returned rays we shall call secondary rays.
The consideration of the nature and manner of production of
these secondary rays suggests some interesting questions, as the
experiments of Sagnac and Langevin show that these secondary
rays differ in their properties from the primary rays which excite
them. So that it would seem that bodies exposed to Réntgen
rays can themselves emit rays which possess many properties in
common with the ordinary Rontgen ray. Thus for example
Rontgen has recently shown that air through which Rontgen rays
are travelling sends out rays into regions carefully screened from
the direct action of the primary rays.
Sagnac, who has recently investigated the properties of the
secondary rays diffusely reflected from metals, finds that though
they resemble the primary rays in not being refracted, they are
absorbed with very much greater rapidity, the secondary rays
being practically extinguished after passing through a centimetre
or so of air at atmospheric pressure. Sagnac found too that the
penetrating power of the secondary rays depended on the nature
of the metal from which they emanated; thus close to the surface
of the metal the secondary rays were more abundant with zinc
than with copper, at a short distance from the surface of the metal
the proportions are reversed, showing that the rays from copper
have more penetrating power than those from zinc. Sagnac
arrived at his results by using the photographic method. Langevin
394 Prof. Thomson, On the Diffuse [Jan. 24,
working at the Cavendish Laboratory has arrived at these and
other results by the electric method.
The following investigations were undertaken in the hope of
throwing some light on the way in which the molecules of a
substance might be conceived to give out Réntgen rays.
Since there is no reflection of the Rontgen rays we cannot
suppose that the secondary rays are produced by an action similar
to that by which light is ‘scattered’ from small particles.
If however we adopt the theory described by the author in the
Philosophical Magazine for Feb. 1898, that the Rontgen rays are
thin pulses of intense electric and magnetic intensity such as is
shown would be generated by the sudden stopping of the cathode
rays, then one way in which the secondary Réntgen rays might be
produced is as follows. Let us suppose that the atoms of the
substance carry electric charges, then when the pulse of intense
electric intensity which constitutes a Rontgen ray falls on these
atoms it will suddenly change their velocities, this sudden change
in the velocity of a charged atom will generate a secondary pulse
of electric and magnetic intensity which on the above theory
would constitute a secondary Réntgen ray. The nature of this
secondary ray is as follows: if a sphere of radius @ with a charge e
is suddenly started with a velocity w parallel to the axis of X,
then the state of the magnetic field can be shown to be as follows.
If P is a point under consideration, O the centre of the particle,
and OP=r, then H the magnetic force at P is zero when the
time t which has elapsed since the particle was started is less
than (r—a)/V, where V is the velocity of light through the
medium surrounding the sphere: when t>(r—a)/V<(r+a)/V,
then .
_ ew sin 0
Hf
ar
where @ is the angle between OP and the axis of X; when
t>(r+a)/V, |
ew sin 0
=]
Hf
the lines of magnetic force are circles with their centres along the
axis of X and their planes at right angles to it. Thus between |
the times t=(r—a)/V and t=(r+a)/V a pulse of intense
magnetic and electric force is passing over P.
Now consider a primary Réntgen ray travelling along the axis
of z; let the electric intensity im the pulse make an angle ¢ with
the axis of X, this intensity will give an impulsive velocity parallel
to itself to a charged particle in the path of the pulse, let this
1898. ] Reflection of Réntgen Rays. 395
impulsive velocity be w. The magnetic force in the secondary
pulse will in a direction making an angle W with the axis of z and
~ at a distance 7 from the particle be equal to
ew i
ao — sin’ sin’ ¢,
while the energy in the pulse will be proportional to
(1 — sin? sin? ¢).
Let us suppose that instead of there being only one ray there
are a large number in which the electric intensity is in different
directions, but uniformly distributed round z, then the energy will
be proportional to
arr?
e*w?
arr?
(1 — }sin® ),
thus the energy when w= 0 or zis twice that when y=7/2. So
that if the secondary radiation arises solely from an action of this
kind the intensity of the reflected radiation in the direction of the
primary rays would be twice that in a direction at right angles
to them.
The intensity of the diffuse reflection in different directions
was tested by the following method. ABCD is a box made of
A FHM B
FG
1 ake ees
C
Fic. 1,
sheet lead, Réntgen rays pass into this through a small lead tube
EFGH and are diffusely returned from the patch KL; pieces of
photographic plates with screens of perforated zinc in front of
them were placed at M and N, at equal distances from the middle
of the patch HK; the diffusely returned rays from HK produced
after an exposure of about two hours photographs on the plates
N, M; the photographs at M and N did not show any appreciable
difference in intensity though a large series were taken with
exposures varying from 2 to 6 hours. Tests were made which
showed that these photographs were made by rays coming from
HK and not from the air through which the primary Rontgen
rays passed. This was done by removing the bottom of the box,
when the effect on the plates was very slight compared with that
produced when the bottom of the box was in its place. Though
the photographic method is not a very delicate test of the relative
396 Prof. Thomson, On the Diffuse [Jan. 24,
intensity of the rays, the results show that the mtensity at M
where wf is small cannot exceed that at NV where w is nearly 7/2
in anything like the ratio of 2 to 1, thus showing that the greater
part at any rate of the effect does not arise in the way suggested.
Some experiments were made to see if there was anything of
the nature of selective absorption of these diffusely returned rays.
In these a plate in the position M was covered with paper, on this
paper two crosses were placed, one of these crosses was made of
thin platinum foil, the other by painting red lead on the paper;
the thickness of the layer of red lead was altered until when the
diffusely returned rays came from the lead sheet at the bottom of
the box the depth of the shadow cast by the red lead was very
nearly the same as that cast by the platinum foil. The bottom of
the box was then covered by a piece of platinum and photographs
again taken: the depth of the shadows seemed to be in the same
proportion as when the rays were reflected from lead, showing that
there is no marked selective absorption.
The absence of refraction in these diffusely returned rays was
verified by the following experiment. A straight slit parallel to the
bottom of the box was cut in the side BC of a lead box, the diffusely
returned rays passing through the slit produced a bright line on a
photographic plate placed outside the box, a thin wedge of alu-
minium was placed between the slit and the photographic plate
and photographs were again taken, the line of light on the plate
was found unbroken by the prism though faint in the part where
the rays were intercepted. The equality of the radiation in differ-
ent directions shows that these secondary rays do not originate by
the method of which the theory is given above. The primary
Réntgen rays ionize the substances through which they pass, and
the rapid ionization in an electric field of a molecule consisting of
positively and negatively electrified atoms will be accompanied by
an electromagnetic disturbance lasting for only a short time. The
general character of this disturbance may be represented graphi-
cally as in the following figures. In the first stage (a) the
Faraday tubes in the external field and that connecting the atom
in the molecule are uninfluenced by each other; in the next stage
(b) the tubes bend towards each other, then they run together
and break away as in fig. (c), and after this stage the atoms in the
molecule are not connected by a Faraday tube and are dissociated.
While these changes are im progress we have a very rapid
movement of Faraday tubes in a space comparable with that
between the atoms in a molecule. This movement of the tubes
will give rise to an electromagnetic disturbance which in con-
sequence of the intense radiation will be almost dead beat and
so equivalent to a pulse of electromagnetic disturbance. The
1898. } Reflection of Réntgen Rays. 397
radiation emitted from ionization will be more symmetrically
distributed than that previously investigated and so there will be
less difference of intensity between the secondary radiation in the
direction of the primary ray and that in a direction at right
angles to it.
Ionization (if sudden) may thus be expected to give rise to
rays having properties similar to those of the secondary Rontgen
rays. E. Wiedemann* has shown that an electric discharge gives
rise to rays to which he has given the name “Entladungstrahlen ” ;
these rays can pass through substances opaque to light and are not
deflected bya magnet. Now the electric discharge is accompanied
+ Pee —
A
B a
+ =
A
Bt
b
bss 2 f
A
B
c
Fig, 2.
by ionization of the gas through which the discharge passes and,
though this ionization is probably not of so sudden a character as
that produced by Réntgen rays, Wiedemann’s experiments seem to
show that it is rapid enough to give rise to rays having properties
analogous to the secondary Réntgen rays. It seems not impossible
that in the case of a complicated structure like the uranium atom
regrouping of the constituents of the atom may give rise to
electrical effects similar to those which occur in ionization and
might possibly be the origin of the uranium radiation.
1 Zeitschrift fiir Hlektrochemie, 11. p. 159, 1895.
VOL, Lx. PT: Vill. 33
398 Mr Willey, Some Zoological Results of a [Feb. 7,
Monday, 7 February, 1898.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
The following were elected Fellows of the Society :
J. H. C, Datton, M.D., Trinity College.
A. H. Ramsey, M.A., Magdalene College.
W. M. FLetcHeRr, B.A., Trinity College.
The following communication was made to the Society :—
Some Zoological Results of a Voyage to Melanesia during the
years 1894—1897. By ArtuHuR WILLEY, D.Sc., Balfour Student.
I. Nautilus. 1. The deposited eggs of N. pompilius were
obtained by me during the months July—September, 1897, in
cages kept at a depth of some 50 to 60 fathoms in Blanche Bay,
New Britain. They differ very slightly in the ornamentation of
the outer capsule from the eggs of V. macromphalus, the pectinate
_ ridges in those of the former species being more frill-like.
2. The otolithic contents of the otocysts of Nautilus were
correctly described by Macdonald’ in 1855 as consisting of m-
numerable minute otocones. Sometimes in preserved specimens
the effect of the preservation appears to be to coagulate the fluid
contents of the otocyst, so that the otocones cohere to form a
solid otolith. This explanation will account for the erroneous
interpretation recently published on this subject.
3. The region of the mantle which secretes the calcareous
septa of the shell is marked off from the surrounding region by
a thickened rim or contour line. The latter was described by me
under the name of the septal contour and figured on p. 170 of the
Quart. Journ. Micro. Sc., Vol. XXxXIx., 1896, together with a repre-
sentation of the pallio-septal arteries. The septal contour has
been redescribed by L. E. Griffin (loc. cit.) as the “ posterior
ventral aponeurotic band” without referring to my account, al-
though the paper containing it is included in his bibliography.
4. The animal of N. umbilicatus has not, so far as I am
aware, ever been examined or even seen by a zoologist before.
I was fortunate enough to obtain one specimen which had been
taken from the surface in the neighbourhood of the D’Entre-
1 Phil. Trans. 1855, p. 277. Macdonald supposed his specimen, which was
obtained off the Isle of Pines, to be N. umbilicatus; but that it was really N.
macromphalus is abundantly evident from his description of the animal even if it
were not already known that he had mistaken the species.
2. BE. Griffin, “‘ Notes on the Anatomy of Nautilus pompilius,” Zool. Bulletin,
Vol. 1. p. 147. 1897
1898.] voyage to Melanesia during the years 1894—1897. 399
casteaux Group, to the east of New Guinea. While the animals
of NV. pompilius and N. macromphalus are almost, if not quite,
indistinguishable from one another, that of WV. wmbilicatus differs
markedly from both, especially in the surface texture of the hood,
which is coarsely areolated, the polygonal block-like areas being
separated by deep valleys.
5. In any attempt to interpret the morphology of the tenta-
cular appendages of Nautilus and the arms of the Dibranchiate
Cephalopods, if function, innervation, and development are re-
jected as evidence of their pedal origin, the only way left open
to approach the subject seems to be by taking into consideration
the general phenomena involved in cephalogenesis. In all other
animals which possess a compound head, the latter is not pro-
duced by elaboration of the pre-existing simple head with its
preoral lobe, but by the incorporation of other parts of the body
into the cephalic complex. Thus while in Arthropods we have
the cephalothoraz, in the Cephalopod Molluscs we have, viewed
from the standpoint here adopted, the cephalopodium.
II. Ctenoplana. This remarkable animal appears to be the
existing representative of the type from which the Ctenophora
and the Plathelminthes diverged; the former being its pelagic
and the latter its littoral descendants. The importance of Cteno-
plana lies in the fact that it presents a transition from biradial
to bilateral symmetry, the transitional feature being its dorso-
ventrality.
Some authorities consider Ctenoplana only as a slightly modified
Ctenophore. From this point of view, however, Ctenoplana loses
much of its interest and all of its importance; but I do not think
that there is sufficient justification for such a depreciatory attitude.
It may indeed be said that Ctenoplana is no more a Ctenophore
on the one hand or a Planarian on the other than Peripatus is a
Cheetopod or a Myriapod. For further details on Ctenoplana I
may refer the reader to my paper in the Quart. Journ. Micro. Se.
Vol. XXXIX., p. 323.
III. Enteropneusta. In Spengel’s great Monograph of this
group there are two theoretical conclusions to which I wish to
refer. The first is that the Enteropneusta have no Chordate
affinities; and the second, that the genus Balanoglossus (sensu
stricto) is the most primitive type of the group. As this genus
is the one which is least capable of beimg compared, in any
detail, with Amphiowus, the latter conclusion, if true, would tend
to confirm the former.
In the section Chlamydothorax of the genus Ptychodera the
gill-slits open freely to the exterior throughout the greater part of
33—2
4.00 Mr Willey, Some Zoological Results of a [Feb. 7,
their length, in Pt. flava throughout their entire extent; in other
words, the branchial sac is freely exposed to the surrounding
water.
Observations made on living specimens of Pt. flava at the
Isle of Pines led me to suppose that this condition of the
branchial sac, with its skeletal supports, which include synapticula
or cross-rods, was more primitive than that in which the primary
bars are fused with the body-wall and the external openings of
the gill-slits are reduced to minute pores. This latter condition
would naturally tend to render the skeletal structures more or
less superfluous, and, in fact, as shown by Spengel, there are no
synapticula in Glandiceps and Balanoglossus.
That this is a secondary loss rather than a primary deficiency
seems to me to be extremely probable, and this view is further
confirmed by the organisation of an Enteropneust which I have
described as a new genus, Spengelia’. This genus, apart from its
own peculiar features, exhibits close affinity to Glandiceps, but
it has synapticula.
Another point which Spengel regarded as evidence of a
primitive nature was the absence of a circular layer of muscles
in the body wall of Balanoglossus. Spengel himself could not
avoid calling attention to the improbability of this defect in
the structure of a soft-bodied animal like Balanoglossus being
primitive, even while vindicatmg his position. In a species of
Ptychodera from Funafuti, recently described by J. P. Hill? as
Pt. hedleyz, Hill found that there was no circular layer of muscles
in the wall of the trunk-region, except at the extreme posterior
end, where it forms the anal sphincter. As this species belongs to
that section of the genus Ptychodera which bears most external
resemblance to Balanoglossus, there is obviously every reason to
suppose that the absence of circular muscles is also a secondary loss.
Such considerations as the above are adduced for the purpose
of proving that Ptychodera (Chlamydothoraz) is the most primitive
and Balanoglossus the least primitive type of Enteropneusta.
IV. Peripatus. Last year I obtained thirteen specimens of
a species of Peripatus in New Britain, which constitutes a new
(Melanesian) type equivalent to the types represented respectively
by the Neotropical, Australasian and Ethiopian species. In the
position of the generative orifice behind the last pair of legs it
resembles the Cape species, in the absence of crural glands it
resembles the New Zealand species, while the facts that the males
have a less number of claw-bearing legs than the females (22 pairs
in the former and 24 in the latter) and that embryos in all stages
1 Q. J. M.8., Vol. xu. p. 623.
2 Mem. Austral. Mus. 11. Pt. 5. 1897. p. 335.
1898.] voyage to Melanesia during the years 1894—1897. 401
of development are to be found in the uteri of one female, indicate
a very striking correspondence with the Neotropical species.
The embryos are provided with a large ectodermic trophoblastic
organ apparently formed by the dilatation of the primary body-
cavity. Of the thirteen specimens only two were males, but the
examination of the older embryos taken from the larger females
showed that the number of legs in the respective sexes was con-
stant. It is probable that the embyros of this species will throw
a side-light on the “placental” development of the Neotropical
species as described by Kenmel.
Monday, 21 February, 1898.
Mr F. DARWIN, PRESIDENT, IN THE CHAIR.
The following communications were made to the Society :
(1) On some differential equations in the theory of symmetric
algebra. By Professor FORSYTH.
This paper is printed in the Transactions, Vol. xvi. Part iv.
(2) The Discharge of Electrification by Ultra-violet Light.
By E. RurHerrorp, M.A., B.Sc., 1851 Exhibition Scholar New
Zealand University, and Coutts Trotter Student, Trinity College,
Cambridge.
The general action of ultra-violet light on the discharge of
electrification has been investigated by many different experi-
menters. Hertz’ in 1887 first drew attention to the action of
ultra-violet light on a spark gap. Wiedemann and Ebert? showed
that the kathode was the seat of this action and investigated the
general effect on high potential discharges. Hallwachs*® and
Righi‘ observed the fact that zinc and other metals became
positively electrified under the action of ultra-violet light. These
results were extended by Elster and Geitel®, who have published a
series of papers on the effect of ultra-violet light in causing
discharge under various conditions and have also® investigated
1 Wied. Annal. xxx1. p. 983. 1887.
2 Wied. Annal. xxx. p. 241. 1888.
3 Phil. Mag. xxvi. p. 78. 1888.
4 Phil. Mag. xxv. p. 314. 1888.
5 Wied. Annal, xxxvitt. p. 40, xxxvill. p. 497, xxx1x. p. 332, xu1. pp. 162, 166,
Lit. p. 433, Lv. p. 684.
6 Wied, Annal. xu. p. 166. 1890.
402 Mr Rutherford, The Discharge of [Feb. 21,
the action of a magnetic field on the discharge at low pressures.
Stoletow? investigated in detail the relation between the current
and electromotive force for the discharge at low voltages and at
different pressures.
Most of these papers have dealt with the general character of
the discharge, but the subject of the nature of the conduction
and of the carrier that discharges the electrification has not been
specially attacked. In a very interesting paper Lenard and Wolff?
investigated the effect of a surface, on which ultra-violet light fell,
on the condensation of a steam jet in the neighbourhood, and
their results led them to the conclusion that many bodies were
disintegrated under the action of ultra-violet light and that the
particles torn off became nuclei for the condensation of the steam
jet. In the light of more recent experiments these results are
however capable of other interpretations.
R. v. Helmholtz? has shown that a steam jet is acted on when
chemical action is going on in its neighbourhood. Richarz* has
shown that Réntgen rays produce condensation in a steam jet,
and Wilson® has recently observed that ions produced under the
action of Uranium and Rontgen radiation become under certain
conditions nuclei for the condensation of water around them. He
has also demonstrated the important fact, which appears to have
been overlooked, that ultra-violet light produces clouds in ordinary
moist air quite independent of any solid body in its neighbourhood.
The presence of this effect must have complicated the effects of
Lenard and Wolff, and the more general results on the properties
of ions in producing condensation seem to show that possibly their
results may be ascribed to the presence of free gaseous ions rather
than disintegrated particles of metal.
It is the object of this communication to give results of
investigations on the nature of the carriers of the negative
electrification produced under the action of ultra-violet light, and
to show that probably the greater part of the electrification is
carried by gaseous ions produced at the surface of the negatively
electrified plate.
In order to obtain a discharge with ultra-violet light, the
light must fall on a negatively electrified surface. There is no
discharge produced by allowing the light to fall between two
plates without impinging on either. In this respect the action
of ultra-violet light is very different to Roéntgen and Uranium
radiation, which produce a volume ionisation of the gas through
1 Journal de Russ. Phys. xx1. 1889. Journal de Physique, 1x. p. 468. 1890.
2 Wied. Annal. xxxvu. p. 443. 1888.
3 Wied. Annal. xxxu1. p.1. 1887. xu. p.161. 1890.
4 Wied. Annal. urx. p. 592. 1896.
5 Camb. Philos. Soc. Vol. 1x. Pt. vii. 1897.
1898. ] Electrification by Ultra-violet Light. 403
which they pass. The question whether there is any volume
ionisation of a gas through which ultra-violet: light passes was
investigated by Henry’ who tried the vapours of iodine and methyl
iodide both of which are very powerful conductors under Réntgen
rays but with a negative result. The result of Wilson that a
cloud is formed in moist air with strong ultra-violet light renders
it possible that there is a slight volume ionisation of the gas
through which the light passes, but the effect appears to be too
small to be determined by electrical means, and in all later
experiments it is assumed that the surface of the negatively
charged plate is the seat of the action of the ultra-violet light
discharge.
If we allow ultra-violet light to fall on a negatively electrified
surface, e.g. a polished zinc plate, since the body is slowly dis-
charged, it seems probable that if the discharge is due to the
convection of the charged particles, these charged particles can
be blown away by directing a sufficiently rapid blast of air across
their path. This has been experimentally shown by Zeleny?, who
showed that a negatively charged gas can be obtained by blowing
past the negatively charged plate when the ultra-violet light was
acting. This gas has similar properties to the charged gas?
obtained by the separation of ions in Réntgen ionisation, for they
readily give up their charge and refuse to pass through a plug of
cotton-wool:
I had independently observed the same fact, and had also
investigated the effects of blowing currents of air by electrodes,
especially from the point of view of determining the velocity of
the carrier of electricity.
Before entering on the general results it is necessary to draw
attention to the phenomena observed by Blondlot and Bichat?.
They found that if an insulated zinc plate was acted on by ultra-
violet light, when all the conductors in the neighbourhood were
connected to earth, the potential to which it could be raised was
increased 6 or 7 times by allowing a blast of air to impinge on the
plate. They found that this action was independent of dust and
moisture. It is.easy in this way to raise the potential of a plate
of amalgamated zinc to 15 volts in a few minutes, although the
potential to which it could be raised under the action of the light
alone was less than 2 volts.
I have also found that the rate of leak of a body charged
negatively is much more rapid when a blast of dust-free air is
directed against it. A plate of polished zinc, charged to — 8 volts,
1 Proc. Camb. Phil. Soc. Vol. 1x. Pt. v1. 1897.
2 Phil. Mag. March, 1898.
3 Rutherford. Phil. Mag. April, 1897.
4 ¢. R. xvi. p. 29. 1888,
404 Mr Rutherford, The Discharge of [Feb. 21,
placed at a distance of 10cm. from a neighbouring plate gave a
rate of leak 12 times as fast as under the action of the ultra-
violet light alone. The blast seems to assist the electromotive
force in removing the negative charge. The presence of this
action must be taken into account in all cases where currents of
air impinge on negatively electrified surfaces.
The following figure (Fig. 1) shows the general arrangement
WS LZ g a NS
EaArTA | | |
of the experiment to show the effect of blowing a current of air by
a negatively electrified plate on which ultra-violet light is allowed
to fall.
A blast of air from a bellows or a gasometer passed between
two parallel plane electrodes B and C, and then through an in-
sulated aluminium cylinder 7. The air before reaching the plates
was free from dust as far as possible by passing through a bulb G
tightly packed with cotton-wool. An are light A was used as a
source of ultra-violet light. The light after passing through a
quartz plate Q, which covered an opening in a metal screen LI
surrounding the arc, passed through a second quartz plate Q,,
through the fine wire-gauze B and then impinged on the metal
plate C, which was generally of polished or amalgamated zine.
The broken lines show the position of insulators by which the
gauze B, the plate C, and the tube 7’ were all insulated from one
another. An insulated wire W passed centrally down the
tube T.
In a particular experiment the plate C was 42 cms. long,
1-5 cms. wide and ‘8 cm. from the gauze B. Since the area of the
rectangular orifice through which the air passed was only 1:2 sq.
ems., velocities of the air of 300 or 400 cms. per sec. could be
readily obtained.
Fic. 1.
eo. =
TR il nie ot te
1898.] Electrification by Ultra-violet Light. 405
Experiment 1.
C was connected to the negative pole of a battery of 8 volts,
the other pole being connected to earth. The gauze B was
connected to one pair of quadrants of an electrometer, the other
pair being connected to earth. All other parts of the apparatus
were earthed. When the arc light was acting the plate C lost a
negative charge which passed over to the gauze B and the electro-
meter needle showed a movement corresponding to
60 divs. per min.
When a rapid current of air was directed between the plates, the
leak to the electrometer was completely stopped. This showed
that the carriers of the negative charge, which had left C, had been
blown out by the rapid current of air.
If C was charged to —24 volts the rate of leak from C cor-
responded to
170 divs. per min.,
but where the blast was in action the rate of leak was reduced to
8 divs. per min.,
or less than 54, of the charge which escaped from C reached the
gauze B; when CU was charged to higher voltages and the blast
kept in action, a still greater proportion of the charged particles
reached the gauze without being blown out. The number of
carriers that reached the gauze could be raised or lowered by
diminishing or increasing the velocity of the blast, the other
conditions remaining the same.
Experiment 2.
We have seen that a whole or part of the charged carriers
can be prevented from reaching the gauze B. It is now necessary
to show what becomes of the carriers after being blown out from
between the plates. The plate C was charged to — 24 volts and
the gauze connected to earth. The aluminium cylinder 7’ was
connected to one pole of a battery of 30 volts, and the wire W
connected to the electrometer. There was no deflection of the
electrometer if the arc alone was acting. If 7’ was charged nega-
tively, then when a current of air was sent between the plates
the wire W became charged negatively. If 7’ was charged posi-
tively there was no appreciable leak to W. This shows that a
negatively charged gas has passed into the cylinder which in the
first case lost its charge to the central wire and in the other to
the tube 7. A very convenient means of testing the whole
charge conveyed with the current of air is to place a plug of
cotton-wool inside the tube, which has the property of completely
discharging the electrification carried with the air.
406 Mr Rutherford, The Discharge of [Feb. 21,
Experiment 3. Discharging power of a metal tube.
If the aluminium tube 7 which was 30cm. long and 1:1 cm.
diameter was connected to the electrometer and the central wire
removed, it was found that the gas gave up part of its charge to
the tube in its passage along it. In an experiment where the
velocity of the air along the tube was about 150 cm. per sec., 4 of
the gas was discharged in passing along the tube. Since the
electrified particles tend to repel one another to the side such a
discharge is to be expected. If the volume density of the
electrification were uniform over the cross section of the tube,
an experiment of this kind on the discharging power would allow
us to calculate the velocity with which the carrier moves under
its own repulsion, but this condition is here not fulfilled.
Experiment 4.
All the electrification blown out between the electrodes C and
B can be collected. In one experiment the rate of leak of C was
observed with the blast in action. Part (1) of the charge which
left C was given up to the gauze B, a part (2) was discharged on
the tube 7’ and the part (3) which escaped was caught in a cotton-
wool collector. The sums of the rates of leak to (1), (2) and (3)
were found to be very nearly equal to the rate of leak of C.
Velocity of the Carrer.
The general experiments on the effects of a current of air
between two electrodes when the ultra-violet light is acting may
be simply explained by supposing that the negatively charged
particles, which escape from the surface C, travel towards the
gauze B with a velocity proportional to the electromotive force
between the two plates.
Let u= velocity of the charged particle for a potential gradient
of 1 volt per cm.,
d= distance between the plates,
1 =length of the plates,
y = difference of potential in volts between the plates.
The time ¢ taken for the carrier to pass from one plate to the
other is therefore given by
1898. ] Electrification by Ultra-violet Light. 407
Now if P=velocity of blast, the time ¢, taken for the current of
air to pass between the electrodes is given by
t = P .
Assuming that the velocity of the air blast is constant over
the cross section of the plates, if ¢, is less than ¢ none of the
charged carriers which leave C can reach the gauze B, but they
will be all blown out with the current of air. We may suppose
the carrier describes a diagonal path between the plates due to
the resultant of the two impressed velocities at right angles to
each other, and unless this diagonal path cuts the gauze B the
carrier will escape.
Let AB, CD (Fig. 2) be the two plates. Suppose the carriers
to be produced uniformly along CD by the action of ultra-violet
light. A carrier starting from C' travels along the diagonal path
CL and gives up its charge to the plate AB. Draw BP parallel
to LC, meeting CD at P. We see that a carrier starting from P
A iL B
ye yee is
—_ oa ue :
a t ”
a Pod
Cc P D
Fie. 2.
will just reach B. All carriers starting from the right of P will
not reach AB but will be carried out by the current, while those
to the left of P will give up their charges to AB. The ratio p of
the number of carriers blown out to the total number that leave
CD is given by
PD
oD”
the distance PD=P .t, where ¢ is the time taken for the carrier
to cross over between the plates ;
Cp.
The ratio p is determined experimentally and P can be measured,
therefore the value of u can be at once obtained.
408 Mr Rutherford, The Discharge of [Feb. 21,
Experiments performed in this way give a value of the
velocity of the carrier at normal pressure of about
1°5 cm. per sec.
for a potential gradient of 1 volt per cm. This method is
however probably not capable of accuracy, on account of the
variation of the velocity of the air across the cross section of the
plates and accidental disturbances due to the violent eddying
motion of the air when velocities of the order of 300 or 400 cm.
per sec. are used. The method is also practically restricted to
the case of air on account of the large amount of gas required
for an experiment, so that I was led to devise a more general
and satisfactory method of determining the velocity of the carrier.
In Fig. 3 the general arrangement is shown: a glass bell-jar
j RQ
a eae Se eT ree | 414
Fie. 3.
was fixed on a base plate CD of zinc through which a circular
opening HF was cut. In the top of the vessel there was fixed
an ebonite stopper through which passed a rod L carrying at one
end a polished metal plate AB. This plate AB was fixed to a
ball-and-socket joint, and could be levelled by screws passing
1898.] Electrification by Ultra-violet Light. 409
through a plate fixed to the rod. The plate AB could be raised
or lowered from the outside of the vessel by a screw. The bell-
jar was fitted down to the base plate with sealing-wax, and the
whole was placed on insulating blocks over a source of ultra-violet
light S, which was either an arc light or a spark gap. The ultra-
violet light first passed through a quartz plate Q,, fixed over an
opening in a large metal screen, then through the quartz plate
Q, covering the opening /F, and then fell on the metal plate AB.
The wire-gauze performed the double function of allowing part
of the light to pass through and yet acting electrically as a plane
metal surface. The plate AB was generally of polished zinc and
was accurately levelled to the base plate. A delivery tube 7’ was
let into the base plate and the whole vessel was made air-tight
to allow of exhaustion.
In order to determine the velocity of the carrier, the rod L
which was insulated by means of the ebonite stopper was con-
nected to one pair of quadrants of the electrometer by the wire
M, the other pair being to earth. The base plate CD was then
connected to one terminal of a 100 volt transformer, worked from
the town mains, the other terminal of which was connected to
earth. When the base plate is charged positively, the plate AB
is charged negatively by induction, and the negative carriers, set
free under the action of the ultra-violet light, start travelling
towards the base plate under the influence of the electromotive
force acting between the two plates. If the plate AB is close to
CD, a large number of the carriers are able to reach CD and give
up their charge before the electromotive force is reversed. All
the carriers distributed between the plates at the instant of
reversal travel back to the top plate, and since the top plate is
charged positively by induction no more carriers are produced
during that half alternation. Experimentally it was found that
there was no leak to the top plate when the base plate was
negatively charged and the ultra-violet light was in action. We
see therefore that when the plates are close together the plate
AB loses a negative charge. This rate of leak will evidently
decrease as the distance between the plates is increased, until a
certain distance is reached, when the plate AB shows no loss of
charge, although the ultra-violet light and alternating E.M.F. are
both acting. When the plate is at this distance the first carriers
liberated when AB becomes negative by induction are able to
travel nearly to the base plate, but before any can give up their
charge, the E.M.F. is reversed and they travel back to the plate
from which they came. All distances greater than this give us
no rate of leak, but it is the object of the experiment to determine
the shortest distance between the plates for which AB shows no
loss of charge. This point is in general fairly sharply defined, as
410 Mr Rutherford, The Discharge of [Feb. 21,
the table below shows, which gives the rate of leak at different
distances from the base plate.
Turns of Screw aces ae ea
1 turn off scale
3 290 divn.
5 220
7 120
8 35
9 2
9:5 0
9 turns of the screw is approximately the shortest distance
between the plates for which the loss of charge is negligible, and
the numbers show how rapid is the decrease of deflection between
7 and 9 turns.
Let w= velocity of the carrier for a potential gradient of one
volt per cm.
d=shortest distance between the plates for which the
leak of AB is zero.
T = time of complete alternation of the transformer.
It is assumed that the E.M.F. at any time of the alternation is
given by #,sin 27 a , where #, is the maximum value of the
alternating E.M.F.
The distance dz traversed by an ion in the time dt is given by
ps Bed ee Bae
d a
Now the distance passed over by the carriers which first set
out is equal to d in the time = :
1898. ] Electrification by Ultra-violet Light. 411
‘, integrating both sides we obtain
or i
The distance d is determined experimentally, and /, and 7 are
constants of the transformer circuit, so that wis known. Since
the electrometer circuit is insulated before the E.M.F. is applied to
the lower plate, the true potential difference between the top and
base plate is less than the potential of the lower plate on account
of the induction effect between the two plates. In consequence
of the rapidity of the alternations the electrometer needle shows
no movement due to the induction effect, so that it is necessary
to determine the correction to be applied when the needle of the
electrometer remains at rest. This may be simply done as
follows :
The two quadrants of the electrometer are insulated from each
other, and then a steady E.M.F. is applied to the base plate. The
electrometer needle is deflected, but is brought back to its original
position by applying a suitable E.M.F. to the other pair of quad-
rants. Let r be the ratio of the applied potential to the potential
V of the base plate. The potential of the electrometer circuit 1s
rV and the true difference of potential between the plates is
(l—-r)V.
The correction is thus made by putting (1 — 7) #, instead of
E, in the equation that determines the velocity.
The following is an example of a determination of the velocity
of an air ion travelling through air,
d=‘8cm.,
T = 4, sec.
Reading of alternating voltmeter 95, the maximum value of
the E.M.F. 4, is therefore given by
II Wes
GOT «hen.
“= ET 1:37.
The correction for induction between the plates was 5 per cent.,
so that the final value is
wu = 1:44 cm. per sec.
A large number of determinations have been made for the
velocity of the air ion, and the mean of the results gives a velocity
of about
1°45 cm. per sec.
412 Mr Rutherford, The Discharge of [Feb. 21,
In these experiments two sources of ultra-violet light have been
used, viz. an arc lamp and a spark between two zinc terminals.
For the spark two large Leyden jars were charged up by a
Rumkhorff coil and discharged through a spark gap of about
‘8cms. In order to get rid of electrostatic effects, the jars, coil,
and spark gap were all placed inside a metal tank connected to
earth. The opening above the sparking terminals was tightly
closed by a quartz plate, on both sides of which fine wire-gauze,
connected to earth, was stretched. This arrangement was found
to screen thoroughly from electrostatic disturbances.
For experiments on the velocity of the carrier the are light is
not nearly so satisfactory a source of ultra-violet rays as the
spark discharge. The arc as a rule gives out more intense
radiation but it has the drawback of rapidly raising the tempera-
ture of the plates and of the adjacent air. In consequence of
this the velocity of the carrier is changed, and the determination
of the least distance of no appreciable loss of charge cannot be
made with certainty. In this respect the spark light is far more
satisfactory and it is alsoa more constant source of rays, but it
has the disadvantage of being an intermittent source of light.
A source of error in the determination of the velocity, which
is difficult to avoid, lies in the irregularity of the E.M.F. from the
town supply. During the daytime, the load on the machines was
light, and there were often rapid alterations in the E.M.F. and
period of the alternations. Another source of error also lies in
the assumption that the electromotive force curve of the alternator
is a sine curve. It is mtended to continue these experiments
and to use instead of the transformer an alternating electromotive
force produced by reversing the sign of a steady E.M.F. by means
of a suitable revolving commutator. It is hoped in that way to
obtain a very accurate value of the velocity under varying condi-
tions of pressure and temperature.
Effects of different metals.
If the theory that the discharge of electrification is due to the
disintegration of negatively charged particles is true, we should
expect to obtain different velocities of the carrier according to
the metal on which the ultra-violet light falls. This point was
tested by replacing the zine plates by similar sized plates of
aluminium, lead, copper, amalgamated zinc and a zine plate
covered with mercury sodium amalgam. Although there were
differences in the rate of leak of these metals due to their different
degrees of sensitiveness to ultra-violet light, it was found that the
distance of no loss of charge was nearly the same in each ease.
The are light was used for this series of experiments, and allowing
1898. | Electrification by Ultra-violet Light. 413
for errors of experiments it seems to be true that the velocity of
the carrier is independent of the metal on which the light falls.
This seems to show that the carrier is produced from the gas
near the plate and not from the metal itself.
Effect of electromotive force.
The velocity of the carrier, i.e. the velocity for a potential
gradient of one volt per cm. is independent of the potential of the
surface from which the carrier sets out.
Experiments were also made to determine the value of the
velocity for different values of the E.M.F. To test this the ultra-
violet light from an are was allowed to shine through a wire-
- gauze on to a metal plate which was much larger than in the
experiments in the bell-jar. By using a suitable transformer,
potential differences, which were measured by a Thomson’s Multi-
cellular Voltmeter, of 365 and 700 volts beside the usual 95 volts
were obtained.
Voltage | d | Correction for induction
|
95 volts | ‘T75 cms. 14 per cent.
BOD Fs. | oe les Ol.
700. , BOT 5; (ero
When the corrections for induction are made, the radius of
the velocities obtained for unit potential gradient are
|
Voltage Velocity |
| i
[Pye echipsey |W Rahs a as
| |
he hee3) sash de arte |
700 | 1:33 |
We see from the above table the velocities are very approxi-
mately proportional to the electromotive intensity between the
VORA 1X. PIS Vill. 34
414 Mr Rutherford, The Discharge of [Feb. 21,
plates. The actual velocity of the carrier when the »M.F. was
700 volts was 450 cms. per sec.
From considerations based on the kinetic theory of gases it
can readily be shown that a carrier of molecular dimensions
carrying an atomic charge attains a limiting velocity in a uniform
field after a very short interval of time and it then moves uni-
formly. No correction therefore need be made for the interval
that elapses before the carrier reaches its limiting velocity.
Effect of pressure on the velocity of the carriers.
The effect of pressure on the velocity was investigated by
means of the apparatus shown in Fig. 3.
The following table shows the results obtained for air :
Pressure Velocity
765 mm. 1:4 cm.
323 3°36
162 73
140 78
95 Lites
58 203
34 33°6
These results show that down to a pressure of 34 mm. the
velocity of the carrier is inversely proportional to the pressure.
As Stoletow has shown, it was found that the rate of leak fora
given E.M.F. increased with the diminution of pressure so that the
results were capable of fair accuracy even at low pressures.
The plates were never separated by more than 1°5 cm. but the
electromotive force employed was much smaller for the lower
pressures. In the experiment for the pressure of 34 mm. only
7 of the voltage of the transformer was used.
If the law that the velocity is inversely proportional to the
pressure holds for low pressures at a pressure of 1 mm. with a
potential gradient of 1000 volts per cm. the carrier would travel
with a velocity of 1-4 x 760 x 1000 = 108 cms. per sec.
1898. ] Electrification by Ultra-violet Lnght. 415
These experiments on the variation of the velocity with the
pressure afford very strong evidence that the carrier of the charge
is of molecular dimensions.
According to the kinetic theory of gases the velocity of a
charged particle of molecular dimensions varies inversely as the
pressure’. If however the particle is large compared with a
molecule, the velocity of the carrier is dependent only on the
viscosity of the gas which is independent of the pressure within
limits. The conclusion to be drawn from these results is that the
carriers must be very small and comparable in size with a
molecule.
Many of the interesting results of Stoletow® on the relation
between the current and the E.M.F. for different pressures on
ultra-violet light conduction can be generally explained on the
hypothesis that the rate of production of the carriers is a function
of the pressure, and that the rate of escape of the negative ions
is dependent on the velocity of the carrier.
It is not my intention here to enter into a detailed discussion
of his valuable results but the fact that the current through the
gas at very low pressures (about ‘002 mm.) is independent of the
pressure seems to show that either there is a slight disintegration
of the electrodes by ultra-violet light or that the presence of
mercury vapour is responsible for the action.
Velocity in different gases.
The velocity of the carrier depends on the gas surrounding the
plates. Hydrogen and carbonic acid were used and were well
dried before passing into the apparatus.
Gas Velocity | Ratio, Air—1
Atay oS Aekrsisttwsce 1-4 1
Hydrogen. ........ 3°9 2°8
Carbonic acid .. ‘78 56
These results were obtained with the use of the arc ight when
the heating of the gas prevented the velocities being obtained
with as much accuracy as desired. The hydrogen ion in hydrogen
1 J.J.Thomson. Brit. Assoc. Report, 1894.
2 Journ. de Phys. 1x. p. 468. 1890.
34—2
416 Mr Rutherford, The Discharge of Electrification etc. [Feb. 21,
travels nearly three times as fast as the air ion im air, and 5 times
as fast as the carbonic acid ion in carbonic acid.
It has been shown that the carriers which are produced under
the action of ultra-violet light have very similar properties to
the ions which are produced by Réntgen radiation. It is also
an interesting result that the velocity of the air ion m Rontgen
conduction is not very different from that obtained in ultra-violet
light conduction. In a previous paper’ it has been shown that the
sums of the velocities of the positive and negative ions in air,
hydrogen and carbonic acid are 3:2, 10-4 and 2:15 cms. respectively.
Assuming for the purpose of comparison that the velocities of the
positive and negative ions are equal, the table below shows the
relative values of the velocities for the negative ions:
Velocity in | Velocity in Ul-
Gas Roéntgen tra-violet light
Conduction Conduction
SANG UR eae i tert 1:6 cms. 1-4
Hydrogen ...... Oy 3°9
Carbonic acid ...| UO ee 78
= = —
Considering the widely different methods used for the deter-
mination of the velocities in the two cases, the comparative
agreement shows that possibly the carrier is the same in the two
cases or in any case not greatly different.
The results obtained in this paper seem to show that the gas
near the surface of the negatively electrified plate is ionised under
the action of ultra-violet light. The positive ion gives up its
charge to the plate and the negative ion is repelled from the
plate. This ion travels through air at normal pressure and tem-
perature with a velocity of about 1-4 cms. per sec. for a potential
gradient of one volt per cm. The velocity of the ion varies in-
versely as the pressure and is different for different gases.
It is intended to continue these investigations on the velocity
of the ions and on the general phenomena of ultra-violet light
conduction.
! Phil. Mag. Nov. 1897.
CAVENDISH LABORATORY,
Feb, 21, 1898.
1898.] Messrs Heycock & Neville, Rontgen photographs. 417
(8) Rontgen photographs of metallic alloys. By Mr C. T.
Heycock and Mr F. H. Neville.
The authors exhibited and described photographs taken by
means of the Réntgen rays through plates of alloy. As the two
metals forming the alloy possess different degrees of transparency
to these rays the photographs show the separation of the metals
that has taken place during the solidification of the alloy. For
example, alloys of gold and sodium containing less than 30 per
cent. of gold are seen to consist of well-developed, very transparent
crystals, which must be pure or nearly pure sodium, imbedded in
a mother substance which solidified last, and which from its com-
parative opacity evidently contains the gold. On the other hand,
alloys containing more gold show very opaque needles of gold im-
bedded in a less opaque mother substance. This mother substance
was the same as that in the first-mentioned alloy; it solidified
after the needles of gold had been formed. Photographs of alloys
of aluminium and gold and of aluminium and copper were shown
which exhibited similar phenomena. The crystals of aluminium
in the alloy with copper were perfect rectangular crosses several
millimetres in diameter. The gold-aluminium alloys showed a
precipitate of Roberts-Austen’s compound of the formula AuAl, ;
the crystals were well-marked cubes and octahedra.
Monpay, 7 March, 1898.
PROFESSOR NEWTON, VICE-PRESIDENT, IN THE CHAIR.
The following Communications were made to the Society :—
The Coral Reefs of Funafuti, Rotwma and Fiji together with
some Notes on the Structure and Formation of Coral Reefs in
general. By J. STANLEY GARDINER, M.A., Gonville and Caius
College, Cambridge.
INTRODUCTION.
HAvING been enabled by means of a grant from the “Balfour
Fund” to join the “Coral Reef Boring Expedition” to Funafuti,
I had the pleasure of spending upwards of three months on
that atoll with Prof. Sollas, who suggested to me the propriety of
comparing its reefs with those of Fiji and other islands in the
vicinity. To Prof. Sollas I am under deep obligations, and any
value that my observations may have is largely due to him.
418 Mr Gardiner, The Coral Reefs of [Mar. 7,
I am also much indebted to Capt. Field and the officers of
H.M.S. Penguin for their great courtesy and assistance at all times.
Returning to Fiji in the middle of August, I left in the
Penguin at the end of the month for Rotuma, where I remained
until the middle of December. Here I was much beholden to
Mr Leefe, the Resident Commissioner, for his assistance and
especially for the loan of his boat and crew.
Coming back to Fiji the second time, after a tour round
Ovalau, I proceeded along the north coast of Viti Levu to
Nathilau. Crossing from there to the Rewa river, I obtained
two canoes and in five days reached Suva, where I remained for
some days, making excursions to the Navua river, the Mbenga
barrier reef and into the neighbouring country. I then spent
a fortnight in Wakaya on the kind invitation of Capt. Langdale,
late R.N. Having received from the Hon. J. Stewart, Colonial
Secretary, an offer of a passage round the Lau Group in the
government 8.S. Clyde, I gladly accepted, visiting the Exploring
Group, Lakemba, Fulanga, Ongea, Namuka and Kambara. On
returning I went to Taviuni, where I spent a fortnight, riding
or walking round the greater part of that island. Ratu Lala,
the native chief, then sent me in his whaleboat to Rambi and
on to Lambasa, which we reached in four days. I next crossed
to Nateva Bay, down which I proceeded, partially by canoe, and
reached Savu-Savu Bay on the third day, whence I proceeded to
Levuka, where I obtained ship to Sydney.
In Fiji I was greatly assisted by Capt. W. W. Wilson, Harbour
Master of Levuka, who took the Clyde round the Lau Group
especially to help and direct me. As Capt. Wilson probably
knows more than any man living about the reefs and anchorages
in the Central Pacific, and most generously placed freely at my
disposal his journals and the mass of imformation he has collected,
I cannot sufficiently express my indebtedness to him. I wish
also to express my thanks to the Hon. W. L. Allardyce, Native
Commissioner; Mr Berry, Commissioner of Works; Mr Turner,
Chief of Customs, Levuka; Capt. Langdale, late R.N.; the late
Capt. Puttnam; Ratu Lala; Mr C. Thomas; Mr W. Reay; Mr W.
Chalmers and many others for their hospitality and aid.
In England I am under great obligations to Prof. Newton,
Mr Adam Sedgwick, Mr W. Bateson, Mr A. C. Seward and
especially to Prof. Hickson, for their encouragement and counsel.
In particular I must thank Mr J. J. Lister for much valuable
criticism and advice.
1898.] Funafuti, Rotuma and Fiji. 419
CONTENTS.
Part LI. The Atoll of Funafuti.
Part II. Rotuma.
Part III. The Reefs of Fiji.
Part IV. The Raised Reefs of Fiji.
Section 1. Viti Levu.
Section 2. The Lau Group.
Section 38. Summary and Conclusions.
Part V. Special Features in the Natural History of Corals.
Section 1. The Structure of a Reef.
Section 2. The Bathymetrical Limits of Coral Growth.
Section 3. The Food of Corals.
Section 4. Conditions affecting the Growth of Coral
Reefs.
Section 5. The Rate of Growth of Corals.
Part VI. The Formation of Coral Reefs.
PART L
THE ATOLL OF FUNAFUTI.
THE atoll of Funafuti was chosen as a typical atoll by the
Coral Reef Boring Committee of the Royal Society in 1896. It
belongs to the Ellice islands, which he to the north of the Fiji
Group, and extend in a broad line from lat. 11° S. to lat. 5° 30’S.,
running almost north-north-west and south-south-east. In the
same line to the north at a distance of about 150 miles lie the
Gilbert islands, which are themselves continued north by the
Radack and Ralick chains of the Marshall islands. All are of
coral origin and many of atoll form.
In the bathymetrical charts, published in the Report of the
Challenger Expedition, the Ellice islands are seen to lie on a
plateau of about 1500 fathoms with the Fijian, Tongan and
Samoan Groups, the whole in a deep of over 2000 fathoms. The
soundings of Captain Field, H.M.S. Penguin, in 1896 proved,
however, that the Ellice islands are separated from this plateau
by depths of over 2000 fathoms, and showed also that Funafuti
rises as an isolated reef in this deep. Further soundings of the
Penguin by Nui, Nukulailai and towards Nukufetau from Funafuti
indicate that these atolls probably rise in a similar manner so
420 Mr Gardiner, The Coral Reefs of [ Mar. 7,
that there appear to be in the Ellice Group a number of isolated
islands rising separately from a depth of over 2000 fathoms.
The atoll of Funafuti (Fig. 1) has a lagoon 12 miles long by
8 miles broad, lying almost north and south. It is of a roughly
oval shape, extending south into a “pocket” about 3 miles deep,
much of the bed of which is uncovered at low tides. Round this
lagoon is a more or less continuous reef, varying in breadth from
+ to 4 a mile in accordance largely with the portion, which has
been turned into land. On the east side is an island 64 miles
long, continued north by two more small islands, Amatuku and
Mulitefala, with narrow breaks in the land between; this main
island bends to the westward about 2 miles from its south end.
Continuing it to the south-west are three other islands, Fatata,
Funangongo and Funamanu, jomed to one another and to the
main island by the reef, which can easily be crossed at low tide.
The next island to the west, Falefatu, is separated from these
by a broad ship’s channel with a minimum depth of four fathoms ;
on the west side of this island there is another similar channel
with a depth of five fathoms. The reef is here continued into
the “pocket,” which extends about 34 miles to the south, and
is largely surrounded by land. On the west side of the atoll
the reef is very broad, nevertheless it has only a few small islands.
To the north-west is another broad ship’s channel through the
reef with a minimum depth of 44 fathoms. On the west side
there are also three channels of 4 fathoms and two narrow some-
what tortuous passages of 11 and 23 fathoms. The north side of
the lagoon has two small islands, Fualifeke and Pava, but while
surrounded by the reef has otherwise no land.
The direction of the wind from March to November is from
the east-south-east, veering completely round in the three summer
months, December, January and February, to the west-north-
west; but while the easterly wind is steady during the greater
part of the year, the westerly wind in the summer is more
irregular and less strong with considerable periods of calm. The
current is due probably entirely to the wind and accordingly
comes from the same direction; I was informed, however, by
several trading captains in Fiji that the set in the summer months
westward is never very great and in calms is lost, giving place to a
slow set eastwards. In agreement with the wind the reef is, save
for the two ship’s channels to the south, continuous round the
east and south sides of the atoll and largely converted into land.
The “pocket,” the projecting southern horn of the atoll, is exposed
fully to the south and east and is almost completely surrounded
by land. The flood tide into the lagoon sets in strongly through
the ship’s channels; but at the same time a large amount of
water is received from the breaking of the sea over the reefs
1898. ] Funafuti, Rotuma and Fiji. 421
WH Pocket”:
FUNAFUTI ATOLL
F LG. 1.
422 Mr Gardiner, The Coral Reefs of [Mar. 7,
between the different islands. The ebb tide, however, can receive
little assistance by the sea water of the lagoon escaping in this
way, so that the out-going currents are much stronger; for some
time indeed after low tide there is still a noticeable current
outwards in these channels. The current too in the southerly
channels naturally sets in stronger, and goes out weaker than
in the westerly ones, as it is to some extent the resultant of the
forces of the tidal and wind currents.
The islands on the reef are generally covered with loose blocks
of reef-rock between which coconut and other trees have taken
root; in most places there is little or no soil. In some parts the
surface shows a flat platform of hard rock with scanty, or no
vegetation ; the largest lies in the middle of Fualifeke, and there
is another on Funafara to the east of the “pocket.” Usually
the presence of this flat smooth platform is concealed by boulders,
among which the trees grow, but I found it existing very generally
on all the islands to the south of the atoll, and by the sides of the
“pocket.” To the east such a flat does not exist, the whole
surface seeming simply to be a mass of loose blocks, the skeletons
of different species of corals and masses of reef-rock.
The breadth of the islands varies from 50—3800 yards, but
of course at their ends they narrow down to mere ridges; their
general breadth is scarcely more than 120 yards. The main
island in its extreme eastern part is considerably broader than
any of the other islands of the atoll, by the village being about
600 yards across. Here there is, however, for the greater part of
the breadth on the lagoon side a deep sandy soil, formed of the
ordinary beach sand, which is found in the lagoon in the vicinity,
mixed with a certain amount of mould from the vegetation, which
grows especially luxuriantly on it. Here too there is what
Professor Sollas has called the “mangrove swamp,” a bare area
in the middle of this part of the island, covered with water at high
tide; to it the sea gains access from the seaward face of the atoll
through three tunnels at its northern end. Its south end is
covered by a fine mud, varying up to 3 feet in depth, with
boulders imbedded in it; these are often of large size and project
in places above the surface of the mud. Partially imbedded in
this mud Professor Sollas has traced a crescent-shaped’ ‘dead
coral reef, constituted almost entirely of two species, one a massive
Porites and the other Heliopora coerulea. For a great part of
the day this floor les bare and dry, the frayed ends of the
Heliopora standing like broken reeds 6 inches above its surface,
and the great clumps of Porites forming a series of stepping
stones of equal height. Neither of these corals stands long
1 Report on the Coral Reef at Funafuti. Nature, Vol. tv. 1897, p. 376.
1898.] Funafuti, Rotuma and Fiji. 423
exposure to the air; on Funafuti they require constant sub-
mergence and we are thus led to regard their upper surface as
marking what was at one time the level of low tide in the swamp.”
The species of Porites, referred to, very closely resembles Porites
arenosa (Esper), a very common species on the shoals in the
lagoon; living Heliopora was only obtained once at Funafuti,
and then from a depth of over 35 fathoms off the southern reefs
of the atoll. The rest of the swamp is sparsely covered with
mud, being formed of a hard consolidated rock, which closely
resembles the rock forming the reef. North of the mangrove
swamp is a marshy pool more or less filled with brackish water,
and there are in the middle of the south end of the same island a
number of such pools; they seem to me to be directly comparable
to the “ barachois” of Diego Garcia’, described by Bourne.
From the sea the mangrove swamp is separated by the
“hurricane beach,” a structure which extends to some extent
round the seaward face of all the islands, but varies considerably
on account of the position of the islands in respect to the atoll,
and possibly from other causes. It is the extreme edge of the
land against which the sea, after passing over the reef, expends its
force. The height of its summit above the sea level at high tide
varies up to 7 feet, but a greater height than 4—5 feet is un-
common. Its top is covered with boulders torn from the reef
facing it, often much rounded and worn by the water. Near
its summit this beach slopes down to the sea at an angle of
about 30°, but towards its base, where it is washed by the tide,
and formed of a hard consolidated coral-rock, it passes gradually
into the flat reef. Its formation along the whole of the main
island is precisely similar to the above, but in the islands to the
south-east of the “pocket” there can scarcely be said to be any
such beach at all, and the land is broken into, and in places
partially submerged at spring tides. On the leeward side of the
atoll generally this beach, or a sudden fall from the land to the
high tide level, exists, but at its base the solid rock cannot be
seen; instead the whole is covered by small rounded fragments
of reef-rock, coral, shells, etc., forming in fact a pebbly beach.
From the hurricane beach the land usually slopes towards the
lagoon with a drop of two or three feet in a few yards, and then a
very gradual slope. To windward of the atoll the islands on their
lagoon sides have usually no sharp fall, the high-tide level at
“springs” being marked by the extension of the vegetation. By
the village, however, the wash on the sandy shore has caused a
well-defined drop of one to two feet. To leeward of the atoll
1 «The Atoll of Diego Garcia and the Coral Formations of the Indian Ocean,”
by G. C. Bourne. Proc. R. Soc. 1888, xi. p. 440.
424 Mr Gardiner, The Coral Reefs of (Mar. 7,
there is a very distinct beach on the lagoon sides of the islands
similar to the hurricane beach of the same islands.
A hurricane beaeh, such as is found on the windward face
of the atoll, could indubitably have been formed by masses of coral
and reef-rock, thrown up by the waves, subsequently consolidating
underneath by the deposition of carbonate of lime on the evapora-
tion of the water at low tide, but under such circumstances the
strata should dip towards the ocean, which piled up the fragments
in the first place. The stratification is not generally visible, but
at the ends of the islands, especially to the south-east of the atoll,
it appears rather to be horizontal. At the north end of Amatuku
there is a section clearly visible of a small cliff about 6 feet high;
the strata are horizontal, but this island is here rather broad and
the cliff stands well back from the sea, continuing for about
50 yards along the lagoon shore. The three islands, Funamanu,
Funangongo and Fatato, have the hurricane beach much steeper
than the main island; indeed the centre one, Funangongo, has
towards the ocean a precipitous fall, in places almost a cliff, of
5 feet, succeeded by a steep boulder-covered beach. On the
top it is not formed of a firmly consolidated rock, but of somewhat
loosely aggregated blocks of coral and reef-rock; the extreme
height here above high tide I measured at 6 feet. The action of
the sea on the coast is plainly visible in fallen shrubs and trees,
undermining the beach, and from the loose nature of the land
above continually causing slips. The beach is strewn with
boulders, which extend considerably below high tide level, and
between tide marks these seem to be joining on to the rock
below by the deposition of carbonate of lime on the evaporation of
the water left on the beach, when the tide falls. On the islands
lying north-east of the “pocket,” a somewhat similar hurricane
beach is found, but it is not so steep; it is, however, consolidated
to a higher level than in these islands, and the horizontal character
of its strata is more distinctly visible.
Under the hurricane beach on the windward side of the atoll
there is an area, rarely more than 15 yards broad, of very rough,
ragged rock with shallow pools of water here and there at low
tide. Outside this is the flat of the reef and its raised outer edge;
these latter parts vary on this face in combined width from 40—
80 yards. As I shall have occasion to refer to these zones
constantly, I shall call them the rough zone, the reef-flat and
the rim. The rock of all these three zones consists of a consolidated
mass of the skeletons of corals and nullipores with shells, sand
and the remains of various marine animals; it is exceedingly
hard and rings to the hammer. On the surface where, exposed
to the air between tide marks, it has time to dry, it is almost
structureless to the unaided eye, but pieces, obtained from under
1898. ] Funafuti, Rotuma and Fr. 425
water by means of a chisel, show clearly its constituents. In the
pools of the rough zone, referred to above, and on the reef-flat
slabs may be here and there raised by a crowbar, used as a lever.
These are found to have been fixed on to the rock below by
means of the living bodies of Tunicata and Porifera, growing to
both, while the spaces between them abound with Polychaeta
Gephyrea, Mollusca and Echinodermata. These slabs, and indeed
the solid rock elsewhere, are in most places much bored by worms,
so that this formed perhaps my most prolific collecting ground
for animals; a considerable amount of muddy sand, formed by
these animals, under the rocks is a general feature. Some of
these slabs have been but recently thrown into their present
positions, and are being consolidated on to the rock below them.
Many others, on the contrary, which could only be raised by
breaking the rock itself, seemed to be due rather to the inwash
of the sea, perhaps removing from under the harder coral, or
nullipore remains, a layer of sandy or softer rock, which had
formerly fixed them to the rock below. Probably both actions
are going on at the same time, the former in the pools of the
rough zone, lying immediately under the hurricane beach, and
the latter on the reef-flat outside its limits. That the effect of
this latter may in time be very considerable was indicated by the
whole beach on the weather side, after a strong easterly gale,
being to some extent strewn with slabs, which, on investigation, I
found to have come from the reef-flat close to the rough zone.
The ordinary range of the tide at springs is 64 feet. At high
tide the hurricane beach at its base is covered with 4 feet of
water; in the rough zone there is a fall of about one foot, and a
sharp fall from this zone of one foot to the reef-flat. The reef-flat
is itself hollowed out to some extent so that it usually has about
8 inches of water on it, but is at the same time cut off from the sea
by the rim of the reef, which stands up about one foot above low
tide. The outer edge is much broken up by fissures (Fig. 2),
which often run for 20 yards or more straight into the reef:
these are joined together to some extent by cross fissures, so that
the rim at low tide appears to consist of a number of great more
or less rectangular flat masses projecting 1—2 feet above the
reef-flat. These are arranged so that there is a distinct edge
running along fairly evenly, but there are outside this on the
weather face of the atoll a number of similar masses extending
outwards for 8—10 yards with a depth over them of 2—3 feet
at low tide. These masses can be clearly seen at low springs,
after the backwash which precedes a breaker, and form the proper
edge of the reef. Off this line there is a sudden fall to a depth
of 3—4 fathoms; in places, however, there is no such fall and
no proper edge, but a succession of masses and buttresses at
426 Mr Gardiner, The Coral Reefs of [Mar. 7,
greater depths further and further seawards. Such a succession
was clearly visible off the south end of the “ pocket,” and in many
places to windward a gradual slope, such as the above, was
indicated by the waves breaking at considerable distances outside
the rim. The fissures (Fig. 2) vary greatly in breadth and shape ;
some are only a few inches broad while others are five or six _
yards. Their depth varies up to 3 fathoms, the average being
at low tide about 14 fathoms where they run through the mm
of the reef. In all, the edges overhang the sides considerably,
and are very thin; indeed, the fissures seemed as if they were
being enclosed by the edges growing out above and meeting one
another, while the channel below was being kept open by the
scour of the tide. In some the edges have absolutely met, and
the presence of the fissure is merely indicated by one or more
blowholes, out of which at low tide is driven a cloud of spray with
each in-rushing wave. Although I carefully examined a number
of these fissures after storms, I never saw any signs of their edges
being broken, and I think that there is no doubt that the flat
surface of the reef extends by their means. The blowholes can be
found almost completely closed, and indeed every intermediate
stage, from what might be termed a boat channel to the solid
reef, formed in such a manner as I have suggested, can be seen
(Fig. 2). At the bottom of these fissures a few small boulders
often lie with a certain amount of sand around and between them.
Occasionally the sides are found to approach one another, and
even to have fused, cutting off from the fissures pools, which, when
the tide recedes, are left full of water.
At the edges of these fissures the reef shows a somewhat
sharp rise of 1—14 feet from the reef-flat (Fig. 2, a). It is here
much pitted on the surface and has a somewhat mammillated
appearance; in the smaller pits Kchini live in large numbers, and
crabs and other animals take refuge in them. Over the surface
there grow small green seaweeds a few inches high, and a small
- slate-coloured species of Zoanthus. Both of these might have
to be carefully searched for, as generally nearly the whole is
covered by white, grey, brick-red and dark green coloured in-
crusting nullipores. The importance of these cannot be over-
estimated; the lime they secrete is always very dense, and
apparently structureless. Its thickness for a single plant is often
very considerable, and nearly the whole reef at the rim I consider
to have been formed by them. It is by means of the growth of
these nullipores that the fissures are bridged, and indeed, by the
use of the chisel, small spaces of a few mches in diameter can
be easily found completely surrounded by these organisms. The
reef-rock of the surface in this position, when broken into, shows
no trace of a coral origin, but simply consists of the lime formed
1898. ] Funafuti, Rotuma and Fijt. 427
by these nullipores. Generally the horizontal thickness of the
lime formed by each plant, as it were, does not seem to be very
great while the total mass is enormous; the thickness of the lime
of some large massive nullipores, obtained by the use of Priest-
man’s grab outside the reef, was between 3 and 4 inches, but
from the reef itself I never saw a nullipore with a greater thick-
ness than 2 inches. What I have termed before the rim of the
reef is really then an area 3—4 feet broad at the sides of these
fissures, but facing the sea about 5 yards across. The waves
break a short distance outside the rim and rush over it, or to
some extent wet it every time they break; the water also rushes
up the fissures, and so great is the momentum behind it, that
it wells over their sides in every direction. The rim generally
extends back all round the fissures, but from the ends of some,
which run especially deeply into the reef, it is absent, these
serving to take the return water, which is poured over the edges
of the others, back to the sea.
Between these several fissures, and between the rim and the
rough zone under the hurricane beach, the reef-flat, before
mentioned, lies. The surface of this zone is very flat and smooth
and covered over completely in its outer parts by nullipores and
other algae. Its level is such that at ordinary low tide the greater
part of its surface is covered over by 8 inches to a foot of water;
its level below the rim round even the most open fissures is
also such that at the lowest spring tides most parts of it are
concealed by a few inches. Nullipores do not thrive on it well,
perhaps on account of the hot sun at low tide, and most of it is
covered by small, delicate, filamentous algae, which give it a very
smooth slippery surface. Holes in it a few inches to several feet
below its general level occur, and in these and on its outer part a
few species of corals are sparingly found. Of these Pocillopora
and Stylophora are by far the most numerously represented, and
in many parts were the only corals obtained from this area.
The species of these genera represented were Pocillopora suf-
fruticosu, P. brevicornis, P. clavaria, P. squarrosa, P. meandrina,
P. glomerata, Stylophora palmata, S. pistillata, S. digitata and
three species which I have named S. compressa, S. lobosa and
S. rugosa. These grow for the most part in clumps, and in this
situation are rarely more than 6—7 inches in diameter, while
3—4 inches with a height of 1—2 inches for the clump is more
usual. Their distribution nowhere is such that they could for a
moment be considered to have any effect practically on the
growth of this part of the reef. The only other species of coral
at all common was a Prionastraea, which was however very local in
its distribution.
The fissures for the reef present the most abundant signs of
4.28 Mr Gardiner, The Coral Reefs of [Mar. 7,
coral life; their sides, where they do not overhang excessively,
often have growths of Pocillopora grandis which markedly shows
positive heliotropism, growing outwards at first from the sides and
then straight towards the light. Their bottoms in any parts,
where they are raised above the general level, and so are above
the scour of the sand, may be covered with corals. From this
position I obtained, as well as various species of Pocillopora, two
species each of Coeloria and Fava and one species each of
Prionastraea, Heliastraea, and Montipora; in addition to the
above, I also obtained Madrepora surculosa and Madrepora haimei
from the north end of the main island, but did not find any other
species of this genus on the windward side of the atoll, although
in Fyi I subsequently found it to be by far the most abundantly
represented on the outer reefs. It would be a misnomer to speak
of any of these corals as being abundant on the outer reef, the
conditions requisite in the fissures being by no means common ;
in any area to be visited there could only be anticipated with any
certainty a few species of Pocillopora and Stylophora and Mon-
tipora incognita (Bernard). Mullepora, which is generally supposed
to grow where the break of the waves is strongest, I only obtained
in this area in a well-protected situation on the leeward side
of the atoll. Under the overhanging sides of the fissures corals
do not grow, though the conditions as to food supply should be
eminently favourable; this may be due to the scour of the water
along the sides, but I think it may also be partially accounted for
by the absence of direct sunlight, the growth in general of the
species of Madreporaria found in these seas showing, according to
my observations, markedly positive heliotropism.
The lagoon shores of the islands on the rim of the atoll have
either a hard pebbly beach corresponding in position, though not
in height or extent, to the hurricane beach with a platform
running off from it into the lagoon, or else a sandy beach usually
tailing off with a similar lagoon platform, or reef. Opposite to
the village there is no such reef, but the sand beach slopes off
gradually into the lagoon, the bottom of which is here covered
by a dense coating of sand. Professor Sollas, in his report’ to
the Royal Society, especially draws attention to the sand: “As
regards the nature of this sand it is important to observe, that it
does not consist of coral débris; this material and fragments of
shells forming but an insignificant part of 1t; calcareous algae are
more abundant, but its chief constituents are large Foraminifera,
which seem to belong chiefly to two genera (Orbitolites and
Tinoporus). It covers a considerable area of the islands, and has
accumulated during the memory of the imhabitants to such an
1 Loe. cit. p. 378.
1898. ] Funafuti, Rotuma and Fi. 429
extent as to silt up certain parts of the lagoon. This and the
abundant growth of corals and calcareous algae, such as Halimeda,
lead to the belief that the lagoon is slowly filling up.” I shall
have occasion later to refer again to this paragraph; here I am
merely drawing attention to it as showing the nature of the sand.
It is only in this one situation that I failed to find a solid gently
sloping platform of rock extending from the islands into the
lagoon; in some places its nature is to some extent disguised
near the shore by a deposit of sand, but its presence is everywhere
clearly indicated. Its surface is smooth, but somewhat broken up
into holes, which generally increase in size with the distance from
the land; it is also in places strewn with boulders. After a
gradual slope, to a depth of about 6 feet at low tide, it commonly
ends in a cliff, or wall, soundings from the edge of which give
depths of 2—5 fathoms, or even more. Such parts of it, as lie
below the low tide level, are covered with green algae, Sar-
cophytum, sponges and foliaceous nullipores; corals too are fairly
abundant on its extreme outer edge. Denser nullipores are also
found belonging for the most part to species with upright plates,
or round mamillated projections; great bunches of the genus
Halimeda are very common. Sarcophytum is found in great flat
spreading masses, but its distribution and that of corals over this
area depend largely on the position of the lagoon-reef in respect
to the openings in the atoll-reef, currents, etc.
The outer reef varies to an extraordinary extent, but every-
where the rim and the reef-flat present similar features to those
already described for the windward side. The inner rough zone
on that side is generally narrow and fairly even in height, but in
places on its inner part just at the base of the hurricane beach
isolated pinnacles of rock occur. These clearly form part of the reef-
rock below them, and consist of similar constituents. The largest
have a diameter of 6 x 6 feet with a similar height; their tops
often to some extent overhang their bases. At high tide they
are washed by the waves, but stand up for 1--2 feet above the
tidal level. By this wash of the waves they are sometimes
eaten into in such a way that the softer rock between the harder
coral skeletons has been removed, leaving the corals freely ex-
posed. The genera Millepora and Madrepora can commonly be
identified ; I also found the laminae of Heliopora. The branches
or laminae of these corals generally grow straight upright in any
position, in which they are well covered at low tide. Their
skeletons, in the few places where I could trace them satisfactorily,
I found invariably standing on these pinnacles in the same
position. Such would not be the case were these pinnacles
formed in a hurricane beach by the consolidation of fragments
and the subsequent solution of the parts of the beach round them.
VOL. EoPr, Vill, 3D
430 Mr Gardiner, The Coral Reefs of [Mar. 7,
Hence I can only conclude that these pinnacles are really due to
an elevation, and are the remains of a part of an old raised reef,
which formerly extended for some distance outside the present
hurricane beach. If this same zone is examined, on the three
islands to the south of the main island, it will be seen to get
progressively rougher with more pinnacles. The middle island,
Funangongo, has no pinnacles, but across this zone there run out
from the hurricane beach great buttresses of coral with fissures
between, up which the waves rush at high tide. These buttresses
are essentially a part of the hurricane beach behind them, and
run out almost to the edge of the rough zone: at ordinary high
tides the crests of most are just awash. The scour of the tide
between these buttresses is very considerable, and accordingly
they are to some extent undermined at their sides and bases. On
the next island to the south, Funamanu, the same characters are
still further accentuated, cross channels sometimes occurring
between these fissures leaving pinnacles outside the buttresses.
Corals in the position of growth are found plentifully on the tops
of these buttresses. The rock forming their greater part is to
the eye structureless, but im places sand and slabs may be seen,
indicating horizontal stratification. The buttresses are continuous
with the lower part of the hurricane beach behind, the upper
part of which is formed by piled-up fragments from the reef in
front. The resemblance of this part of the dry reef to the extreme
outer edge of the living reef, as it at present exists, is very extra-
ordinary. Every stage, from the pimnacles on the extreme
windward face to this structure, can be traced, and I do not think
there can be any doubt but that these pinnacles once formed
part of a similar structure on the weather face, the greater portion
of which has been washed or dissolved away.
On Mateika, Luamotu and Funafara, an almost exactly
similar rough zone to that of Funamanu was found; but to the
south of the “pocket” this zone is about 70 yards broad and
very much as described for the windward side of the atoll, save
that it is rougher and more strewn with boulders, which the seas
have apparently not been powerful enough to roll up. together
to form a hurricane beach, as in fact none such can be said to
exist. On the outer sides of the leeward islands the same zones
are found, but generally the outer rim is less well defined, while
the rough zone is exceedingly broad and rugged. Commonly the
reef-flat is 30—40 yards across, the rough zone being about twice
as broad.
Horse-shoe island, or Fuafatu, on the leeward side exhibits all
these characters in its reef very well. The rim is distinct, but its
fissures are less numerous and deep than to windward; the reef-
flat is about 35 yards in breadth and the rough zone about double
1898.] Funafuti, Rotwma and Fiji. 431
that amount. Then there is a steep beach of rounded pieces of
coral-rock, shells, etc. On the island itself there is a considerable
amount of sand with a very small, though distinct, sandy cliff
by the lagoon with a steep beach of shingle and sand. The lagoon
reef has a maximum breadth of about 120 yards with a steep drop
into about 4 fathoms of water. The sandy beach is not nearly so
well marked in the bay, which gives it the name of Horse-shoe
island, here being formed rather of a consolidated breccia, which
is not on the surface very firm. It can be seen to consist of coral
fragments, sand, and a large number of Y’ridacna and other shells.
Neither the coral skeletons nor the shells are in the position that
they naturally live in, but both dip towards the lagoon, and no
doubt there is a formation of rock going on here between tide
marks by the consolidation of these fragments. The greater part
is not exposed even at the lowest spring tides, so that we have
here the consolidation of a breccia both between tide marks and
under the water.
Small pinnacles are by no means uncommon on the outer
rough zone to leeward: they are exactly similar to those of the
windward face, but are situated generally close to the outside
of the zone, which differs also in being much broader and often
strewn to a great extent with massive boulders. Some of the
pinnacles are not so well defined as belonging essentially to the
rock, of which this zone is composed, and seem to be rather masses
of the conglomerate, now being formed outside the reef, thrown
up on it by strong gales or hurricanes; such are commonly
called “negroheads,” and have been well described by Dana. One
part of the reef between two of the islands, which I was un-
fortunately prevented from visiting owing to a rough sea, appeared
to have a considerable number of such fragments. It is remark-
able that if there are “negroheads” on the leeward reefs, there
should be none on the reefs to windward, against which the force
of most of the gales is broken. Either they are only thrown up
in bad cyclones, or hurricanes (which always strike to leeward),
an almost impossible supposition, or the growth of these masses is
firmer to windward. I consider that such masses would be worn
away, and broken up much quicker to windward of the atoll than
to leeward, and I think, too, that the growth of the reef outwards
goes on faster likewise, so that the masses of reef forming outside
should be fixed more strongly, and be more firmly built to
windward.
To the north of the atoll, are the two islands, Pava and
Fualifeke, separated by a narrow channel from one another, but
at low tide thew rough zones are continuous. Towards the other
each sends out a sand bank, but these are separated by a pool
with about three feet of water at low tide. Off these islands
35—2
432 Mr Gardiner, The Coral Reefs of [Mar. 7,
(Fig. 3), the rough zone is extremely broad being rarely less than
100 yards, while the reef-flat is only about 30 yards. There is
here practically all along a sudden drop of two feet from the rough
zone to the reef-flat, and along this edge there is a line of small
pinnacles. The -hurricane beach is formed of coarse shingle and
shows very distinctly in its abrupt fall the height to which the
tide rises. Towards the lagoon the beach is sandy ; below this the
lagoon platform is distinct. In the small lagoonlet, between the
two islands, there is found a sandstone, the strata of which dip
slightly towards the lagoon. It is apparently a true beach sand-
rock formation and only occurs in this position. I have appended
a section (Fig. 3) across the island of Pava, showing the general
features of the rim of the atoll here.
The reef, except where it is broken by the deep channels before
mentioned, is continuous round the whole lagoon, and connects all
the islands with one another. The rim and reef-flat show no
discontinuity, the reef-flat, continuing between the islands, and a
little lagoonwards ending in a straight cliff exactly similar to that
of the lagoon platform of the islands. The reef between the
islands slopes a little towards the lagoon, so that, even at extreme
low tide, a small quantity of water makes its way over it into the
lagoon instead of flowimg out again through the fissures, which
run through the rim. Probably owing to the difficulty of fixation
found by the larvae, few corals grow on the reef in such a position.
To leeward the reef is often very broad, as indeed are the inter-
spaces between the several islands, and is generally exposed
slightly at extreme low tides. Often its lagoon edge extends
continuously with that of the lagoon platform of the islands, and is
much broken up into knolls and patches, on which corals and
nullipores flourish luxuriantly. South of Fuafatu, the reef has a
distinct channel in its middle a few fathoms deep, extending along
for some distance it consists of an outer reef with a distinct row of
pinnacles marking its position at low tide, and an inner reef, a
broad flat platform, a continuation of the lagoon reef of the island
itself. South of this both reefs have a distinct but narrow passage
to the ocean beyond; this passage through the outer reef is
nothing more than a long fissure with a depth of about 24 fathoms,
and is just broad enough to take a boat through. North again of
the same island and generally to the westward, the reef has a
depression in the centre, but it is not usually more than a few
feet deep.
The shoals in the lagoon commonly on their upper surface,
resemble very closely the inner parts in relation to the atoll of
the lagoon reef, and the same species of coral are found on both.
About the centre of the lagoon is one large shoal, and there are
many others, which lie mostly on the windward side and towards
433
Funafuti, Rotuma and Fiji.
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434 Mr Gardiner, The Coral Reefs of [Mar. 7,
the “pocket.” The greatest depth of the lagoon is 30 fathoms.
The bottom of the lagoon, if the shoals were removed, and the
whole elevated, would be a great plain surrounded by a ridge
sloping steeply up to a line of perpendicular cliffs broken only at
the few deep ship’s channels; on this plain the greatest heights
would be from 20—30 feet. The shoals in the lagoon do not vary
greatly in depth; indeed most can be easily discerned by the
break of the sea on them at low tide, if the wind is at all fresh.
In dredging I searched especially for deep shoals, to find out if
they had any growth of organisms which might be expected, in
course of time, to bring them up to the surface; I passed over
several, both with the dredge and tangles, but I obtained nothing
from them, nor were my dredges ever caught up, as they always
were every few yards on the shallow shoals. This shows that
their surface is smooth and regular. They seemed rather to be
gently sloping eminences on the bottom of the lagoon than shoals
growing up to the surface. One near the large ship’s channel
to the south was perhaps an exception, as the dredge had to
be tripped several times, when I went over it, and subsequently I
lost a large tangle on it in 11—12 fathoms of water. Most of the
shoals have, however, only a few inches of water and are fairly flat
topped, without any central depression; they extend less to
leeward than to windward, or in other words such summits, as
they have, are to leeward. They slope gently at the sides to
3—4 fathoms, succeeded by a cliff to a depth of 10—12 fathoms,
the normal depth of the lagoon being reached within 100 yards of
their edges, close up to which I have often obtained soundings of
14 and 16 fathoms. In the shallower water to windward, these
shoals can often be seen to overhang their bases, and to be mere
mushroom heads. Corals grow most luxuriantly at the sides
where they slope down before the cliff is reached, but many also
flourish on their summits. Pocillopora is very rare, but two
varieties of Millepora flourish, one near the openings in the reef,
and the other, a massive brown lamellar variety, on nearly all
the shoals of the lagoon. There is never on any shoal a great
variety in species, though on some the total quantity of coral is
very considerable, and often exceeds in amount the nullipores
growing on the same shoal. A considerable part of the surface is
to be found on all the shoals covered by species of Sarcophytum
and Halimeda. Of corals, the genera Favia and Madrepora are
the most abundant in species, while Porites arenosa (Esper) with
several varieties is the most common coral, and in many places
forms large masses several feet in diameter and of great thickness.
The genera Montipora, Coeloria, and Astraeopora are very local in
distribution, often assisting very materially.
Between the patches and knolls of rock outside the lagoon
1898.] Funafuti, Rotuma and Fiji. 435
platform, the bottom is generally covered by a sand which is
similar in all respects to the sand described by Professor Sollas.
It does not extend far mto the lagoon off these reefs, and the
arming of the lead usually comes up clean, or only contains a few
of the segments of different species of Halimeda. To leeward of
all the windward islands, sand is found most abundantly, but only
by the main island does it extend more than a couple of hundred
yards into the lagoon where, however, it runs out about 14 miles
in a bank with about 17 fathoms of water, the breadth of which a
mile out from the shore is only about 250 yards. It seems to me
to be deposited by an eddy meeting here, caused by the rising and
rushing of the tide over the reefs to the north and south of this
island. These currents sweep up and down along the coast, the
lagoon reefs surrounding which are notably free from mud and
sand. The sandy part of the island by the village, I think, has
been formed by the deposition and washing up of sand by this
means, and, if any reliance can be placed on the reports of the
natives, the lagoon is here evidently silting up.
In dredging, I took bearings across the lagoon from the village
in three directions, besides trying off certain islands and in
particular localities; I also took a series of soundings at the same
time to find out the nature of the bottom over which I was passing.
The dredges were made by the Zoological Station at Naples, the
one with a net and the other a canvas bag. The result showed
that the bottom generally must be a flat surface of hard rock, as
repeatedly nothing but a few segments of Halimeda were brought
up, and the dredges, while they could be felt on the rope working
along the bottom, met with no hindrances. Near the shoals
masses of dead coral were occasionally obtained, but living corals
never. I cannot agree with Professor Sollas that there is any
evidence that the lagoon of the atoll is filling up, except in the
one position opposite the village. Although I dredged over a
great part of the surface, I found no traces of coral growth on the
bottom and no shoals, with a few fathoms of water which might
be supposed to be coming up to the surface, and I can confidently
assert that there are no considerable banks of sand in the lagoon
other than the one already referred to. Undoubtedly there should
be in some parts a considerable deposition of the skeletons of such
an alga as Halimeda, but of such I found no traces. Either it
must be consolidated with the bottom, or it must be washed out of
the lagoon, or it must be dissolved. I have seen no evidence of
such a consolidation as this taking place anywhere in the islands
of the Central Pacific, and I believe it does not occur; if it is
possible for it to take place at all, the other forces must act before
it has had time to consolidate.
There is no doubt that many of the islands on the rim of the
436 Mr Gardiner, The Coral Reefs of [Mar. 7,
atoll are being washed away. I have already noticed the under-
mining of the pinnacles on the outer reef, and the action of the
sea on this reef generally. Some of the breaks, between the
different islands, seem to have been but recently formed, and the
cliff on Amatuku, before referred to, shows that the action is still
going on. Tengako is a part of the main island to the north
joined by a low, bare sand-bank about twenty yards broad, across
which in a big gale the waves would break. The natives state
that this area was once covered by coconut trees. Additional
evidence is furnished by Afualiku a small island west of the north
entrance; it has now only one living coconut tree, but shows the
remains of several others which have fallen over through the
approach of the waves.
Reference has been made before to the character of the reef
just outside the rim. Masses of reef-rock with fissures and cross
channels extend out for several fathoms; in places, down to
depths of 10—12 fathoms, the bottom is similarly formed. These
masses are ‘covered with encrusting nullipores, which seem
gradually to be joining them on to the rim and extending the reef
further seawards. I could find no signs of their having been torn
up, or washed away, except in a few negroheads on the leeward
reefs of the atoll, and it necessarily follows, as they are completely
protected from solution by growing organisms, that they must be
stationary, or growing upwards and outwards. We have thus the
islands of the rim of this atoll being washed away, while the reef
round them is gradually extending itself further and further
seawards.
Professor Sollas has given, from the soundings taken by the
officers of the Penguin, a section’ of the external slope of the
atoll, but the fall between 15 and 40 fathoms is by no means
always so rapid. Off Falefatu, between the two southern en-
trances, the fall from 15 fathoms was fairly gradual down to 40
fathoms, and I was able to take a haul with the swabs without
going into a less depth than 35 fathoms. There was also off
Fuafatu a broad flat with a depth of about 8 fathoms, on which
the Penguin anchored on several successive nights. A considerable
number of species of coral were obtained on the outer slopes in
depths down to 35 fathoms, but it was impossible to use dredges
on this area without a greater force than the steam launches of
the Pengwin possessed, and so no knowledge of encrusting or
massive species could be obtained. From 35 fathoms I obtained
one small piece of Heliopora, a discovery of great interest as,
while its corallum is exceedingly abundant in the mangrove
swamp, it was only obtained alive at Funafuti on this occasion ;
1 loc. cit., p. 375.
1898. ] Funafuti, Rotuma and Fir. 437
its general habitat seemed to me in Fiji and Rotuma rather to
be on the tops of the reefs, and in the boat channels of fringing
reefs, than in the deeper water outside the reef, or in the
lagoon.
From the steep outer slopes of the reef, between 40 and 100
fathoms, the swabs brought up only a few solitary corals with a
considerable number of fragments of several species of Gorgonacea.
Nearly all these hauls, from the outer slope, produced a number of
loose pieces of stone, most of which had encrusting nullipores
growing on them. In one haul, made up the reef by the Penguin
to 75 fathoms, there were upwards of 30 such pieces none of which
showed any signs of fracture, and nearly all were to some extent
encrusted by these algae. From these dredgings the steep slope
would seem to be formed by the talus of the reef, its angle
75°—80° being apparently the angle at which shingle will lie
at such a depth under the water. The presence of nullipores
growing at depths greater than 75 fathoms is of extreme im-
portance ; the observation, however, requires further confirmation.
In all, the swabs were hauled eight times at a greater depth
than 40 fathoms; the result of six of these hauls I examined and
im no less than four of them encrusting nullipores were present in
the living state on stones brought up; the fifth haul was to a
depth of 105 fathoms, and the sixth only brought up a few pieces
of Gorgonacea.
How such an atoll as Funafuti has been formed can only be a
matter of conjecture in the present state of our knowledge; the
bathymetrical limit of any single species of coral is unknown, and
our knowledge is limited with regard to the multifarious conditions
affecting coral and nullipore life. I have succeeded, I believe, in
showing that there has been, in the case of Funafuti, an elevation.
Professor Sollas, mainly from the evidence of the Heliopora reef
which he very carefully examined in the mangrove swamp,
suggests an elevation of at least four feet. I have pointed out
that smooth flats almost bare of vegetation exist in different
islands of the atoll; now, unless these were originally part of a
reef-flat, I do not see how they could have been formed. In the
raised reefs of Viti Levu, Fiji, I could find no such consolidation
of fragments to flat, hard platforms, such as these, having taken
place above water, and reefs covered over by a fathom or more
of water at low tide do not exhibit any signs of such a platform.
As some of these flats are 5 feet above high tide and the existing
reef-flat is 5 feet below, these would require an elevation of the
whole atoll of at least 10 feet. The edge of the hurricane beach
is simply the edge of these flats, perhaps close to the rim of the
former reef, where it abutted against the sea; the term, hurricane
beach, is then clearly a misnomer, as none, such as is found on
438 Mr Gardiner, The Coral Reefs of [Mar. 7,
other atolls, can properly exist. Considerable denudation and
wearing away by tidal action has certainly gone on, and I think
that its amount is shown by the extent of the rough zone, the
pinnacles and buttresses left being the remains of harder, viz.
coral-formed parts of the reef. Sand enters considerably into
the formation of the islands to leeward, and atoll reefs generally,
such as I suppose the atoll of Funafuti to have been before
it was elevated, are not so high to leeward as to windward, so that
I see no difficulty in the width of this zone there. From the
position of the pinnacles it is necessary to suppose that the
animals, or plants with the hardest and most durable skeletons,
i.e. the corals, were then living on the extreme edge of the reef in
the full force of the breakers, as they are declared by Darwin to
have been doing on the reefs of Keeling Atoll, when he visited
them. The formation of the present reef would of course be
subsequent to this elevation.
The evidence from the facts, bearing on the theory of formation
of coral reefs, collected at Funafuti admit of four conclusions :—
(1) The atoll has been elevated about 10 feet. (2) The land is
now being washed away, the extent of the erosion being shown to
some degree by the breadth of the rough zone. (3) The reef
seems to have been mainly formed by the growth of nullipores,
which are now building up masses outside the rim and adding
them on to the reef, causing its extension seawards. (4) The
lagoon does not seem to be filling up to any appreciable extent
by the growth of shoals, etc., and solution is indicated by the
characters of its slopes and floor.
PART IL.
ROTUMA.
The island of Rotuma, situated in lat. 12°30’ S. and long.
177° 15’ E. is about 260 miles distant from the Great Barrier Reef
of Fiji, the islands of which group form its nearest high land.
It rests on a plateau 1500 fathoms in depth with the Fijian and
Tongan islands, extending to the west to the Santa Cruz Group.
The island is volcanic with hills ranging up to 900 feet in height,
and there are no less than seven craters, the appearance of some
of which leads me to believe that they have not been long inactive’.
From these hills broad lava streams can be traced to the sea and
along the beach, except where they are covered by a deposit of
| Vide ‘‘ The Geology of Rotuma,” Quar. Jour. Geo. Soc. tiv. pp. 1—11.
1898.] Funafuti, Rotuma and Fiji. 439
beach sand; the angle of their slope for 500 yards inland is rarely
more than 3° or 4°. The coast is fairly even with a complete
absence of the “long points and deep fiord-like bays,’ which,
according to Dana, would on a volcanic island give indubitable
evidence of subsidence. Two miles from the west end the island
narrows down to an isthmus about 100 yards broad, completely
covered with sand. The rock to the east, a recent lava, slopes
gradually down to the beach, but to the west the isthmus is
bounded by the perpendicular cliffs of two basaltic hills, Kugoi
and Kiliga; these are undermined considerably at their bases
owing to wave action at the present tide level, proving that the
isthmus at one time did not exist. There is also a deep pool,
300 yards across, with 4—6 fathoms of water and precipitous
walls, within the reef to the north, directly in the line joining the
deepest passages through the reefs to the north and south of the
island in this situation. I have no doubt that there was once a
deep channel across here, which has closed up, as there could have
been no current to keep it open.
The only other rock found besides the recent lava and basalt
is a voleanic ash, which forms the islands on the reef and three
hills at the west end, of which Sororoa alone abuts on the sea.
Where the basalt of Kiliga and the ash of Sororoa and the reef
islands face the sea, they end nearly perpendicularly, the cliffs of
Sororoa being over 700 feet high. On the island I failed to find
any marine deposit, or any evidence of any change of level, so
that, to explain the manifold conditions of its reef, recourse to
such would, I believe, be irrelevant. I consider too that the
extensive beach sand-flats could only have been formed in a
stationary period. Every variety of fringing reef is found, and I
shall endeavour to indicate by a brief sketch of the characteristics
of the reef in different situations the method of formation of a
fringing reef and the first stages in the change from such to a
barrier condition.
About three miles to the west of Rotuma le three islands
Hoflewa, Hatana and Uea in a line from south-west to north-
east ; of these Hoflewa and Hatana are of recent lava while Uea,
which is 900 feet high and surrounded by cliffs, is formed of
ash-rock. Between Uea and Hatana is a shoal Hofhaveanlolo,
awash at low tide; its top is flat and completely covered with
incrusting nullipores with no growing corals. The short distance
in which the breakers rise, together with the deep-coloured water
around, show that its walls are almost precipitous, and indeed with
a 50-fathom line I could obtain no soundings about 50 yards from
its edge.
Hoflewa is a precipitous horse-shoe shaped rock open to the
west-south-west with a cleft, extending from the summit to the
440 Mr Gardiner, The Coral Reefs of [Mar. 7,
sea, about 4 yards broad at the base. There is no shallow reef of
any sort and, although the rock at the sea level is covered with
nullipores, these have nowhere attained a thickness of more than a
few inches. The concavity, which is very shallow, is covered with
great masses of rock with deep fissures between, leaving a channel
to the cleft through which the water rushes with great force.
These masses can still be seen for a short distance outside the
mouth of the horse-shoe, but while the surface of the inner masses
is studded with corals, here their summits are completely covered
with nullipores, only a few colonies of Pocilopora, Madrepora
and Millepora growing on their sides. Around the island to 15
fathoms these masses and ridges continue, but after 25 fathoms in
afew yards no bottom was obtaimed with 50 fathoms; the slope,
however, is not quite so rapid along the lime of the three
islands.
Uea has no reef, but, where the cliffs pass into the water,
nullipores grow freely and have in many places formed a platform
at the low-tide level, extending out for a few yards, dropping off
almost perpendicularly into 20 fathoms. In one position where a
stream has cut its way down to the sea, a broader platform has
been formed by these algae, which do not seem in any way affected
by the fresh water.
Kiliga Point and the islands of Solkopi, Sol Onau and Afaga
present in places the same features as Hoflewa and Uea, but off
Afaga the reef broadens. At its north end there is no platform
of any sort; then to the south at low-tide level a flat, smooth
platform succeeds, covered with nullipores. Having attained a
breadth of about 10 yards, it commences on its mner side to be
slightly hollowed out, forming a channel. The platform continues
to the south, retaining a constant breadth of about 9 yards but
with its outer edge raised about 8 inches above the low-tide level,
while the channel increases with the breadth of the reef, giving
rise to a pool with about 3 feet of water at low tide between the
island and the platform, in which fissures have now appeared,
running in for a few yards.
Off the cliffs of Sororoa the reef is only about 25 yards broad,
and consists of a channel about 4 feet deep and a platform 8 yards
broad; but, while the channel off Afaga is cut off from the sea,
it is here directly connected by a deep, broad fissure, to which a
strong current sets at ebb tide. Perhaps owing to this, it is
devoid of all coral growth and more or less covered with nullipores,
while the pool off Afaga has the same species of coral as were
found on the reef-flat elsewhere. The cliffs behind are in no way
undermined, being indurated with carbonate of lime and extremely
hard.
Round the most westerly point of the island the reef is similar
1898. ] Funafuti, Rotuma and Fiji. 44]
in all essential respects to that off Sororoa, but its breadth is
about 50 yards and its channel has a depth of 6—9 feet. The
platform attains a breadth of about 12 yards, and on it an outer
rather higher part can be distinctly recognised. No fissures
reach through the platform and, as each breaker drives a large
amount of water over it, there results a strong current to passages
to the east and south. A few Prionastrea and Madrepora grow
on the platform among incrusting nullipores, but there are none
in the channel and few nullipores, most of the surface being
covered with low green algae.
As the edge of the shallow reef lies further from the shore,
the platform gets broader, as 1s well seen off Lopta. A distinction
into two parts is now marked, an outer 5—6 yards broad about
9 inches above and an inner at the low tide level. The division
is still more obvious in the reef between Solkopi and Pepji, where
the outer is about 8 yards broad and the inner 30 yards. These
parts, as they seem homologous to the rim and reef-flat at
Funafuti, are accordingly so named here. As the reef-flat
broadens, fragments, torn from the rim or the reef outside, are
thrown on its inner side so that it is itself divided into two parts,
the outer of which is equivalent to the reef-flat proper of an atoll,
and the imner to the piled-up masses of reef-rock, which in an
atoll might be supposed to form the land; the latter is termed the
boulder zone. A section (Fig. 4) then of the reef to the north
of the island or off Noatau, where it is about 500 yards broad,
presents four zones which with their characteristics are as
follows :—
(i) A BOAT CHANNEL (Fig. 40b) extending out for about
250 yards from the shore with a greatest depth of 8 feet at low
tide. Its bottom is covered by a thin layer of sand and mud over
a hard well-consolidated rock, formed of nullipores, corals and
sand. The sand is found principally near the beach and is the
same as the beach sand, while the mud, which lies towards the
outside, is much finer, beg formed mainly by boring worms and
molluses. Halimeda is very abundant, but massive nullipores are
not found; corals do not grow near the beach, but the remainder
of the channel is studded with large clumps up to 20 feet in
diameter. Of these Heliopora and a variety of Millepora are very
common in clusters 5---6 feet across, consisting of parallel lamellae,
arising from broad and firm bases. Symphyllia, Coeloria, Favia,
Astraeopora, Porites and Montipora form large masses, which
after they have reached the surface die in the centre, but extend
at the periphery so as to overhang for several feet. They are
then hollowed out by various boring animals, but their edges
extend evenly outwards a few inches below the low tide level,
so that even at spring tides the living polyps are not exposed.
442 Mr Gardiner, The Coral Reefs of [ Mar. 7,
(ii) Outside the boat channel is the BOULDER ZONE (Fig. 4 cc)
formed of fragments, torn off the reef outside and piled up for
1—2 feet above low tide level with isolated boulders 2 feet
higher. It is not generally well-defined except on the windward
face, its greatest breadth here being about 70 yards. It is in
reality a layer of boulders, lying on the edge of the reef-flat,
which here commences and up to which the boat channel gradually
for some distance shoals ; it is separated merely for convenience
as it should properly be described with the next zone.
Undoubtedly these boulders have been broken off and piled up
by the sea, but after a severe easterly gale the examination of a
part, well hunted over on several occasions, showed but few
additions’.
(iii) The REEF-FLAT (Fig. 4 dd) consists of a smooth platform
of reef-rock with a depth varying from 1 —3 feet below low tide level.
As it is cut off by the boulder zone from the boat channel and by
the rim from the sea, it always retains at low tide approximately
the same depth of water. Its bottom varies enormously, in some
places being smooth and almost bare of corals, but in the position
of the section, where it is about 60 yards broad, growing corals
cover about 25 per cent. of its surface. Madrepora are extremely
abundant, adapting themselves to the depth of the water by
spreading out horizontally; of this genus I obtained 9 species
from this area, of which Madrepora rotwmana is by far the most
abundant. Other genera represented include Pocillopora, Stylo-
phora, Pavonia, Coeloria, Montipora, Prionastrea, Plesiastrea,
Heliastrea and Favia. Incrusting nullipores are absent except for
a few yards on the outer side.
(iv) The last zone slopes up to the RIM (Fig. 4, e and Fig. 5)
but is separated from it by an abrupt rise of 6 inches, for a few
yards above and below which the reef is covered by white nulli-
pores. A platform, gradually sloping upwards, succeeds, here
about 6 yards broad with upwards of 5 per cent. of its surface
covered with Prionastrea, Pocillopora and Stylophora of low
growing species, between which the surface is almost hidden by
white, pink and red nullipores. Fissures commence at the outer
side and run through the crest of the rim, which is about 4 yards
broad and presents the same appearance as the extreme edge of
the reef at Funafuti. The fissures, however, are narrower and in
no way drain the reef-flat ; their sides, too, do not overhang.
Outside the rim the reef has a slope of 10°—15° for about
15 yards, but is much broken up into buttresses, masses and
ridges, which extend as deep as the bottom can be seen. Sound-
1 T was informed by the natives that about 1881 most of the boulders were swept
away in an hurricane, and that the zone has only been gradually reforming since.
1898. ] Funafuti, Rotuma and Fiji. 443
ings in 20—40 fathoms showed that they further occurred to this
depth, as after resting the lead constantly fell off into a depth
greater by 2—3 fathoms. These masses to a depth of about
16 fathoms have a most striking appearance to windward from
the brilliantly coloured nullipores, which cover them, corals being
rarely seen. North of the island, where the breadth of the visible
zone is greater than elsewhere, corals are more abundant, growing
principally on the sides of the buttresses, between which the
bottom is covered with sand. Off the western islands and to
windward there is a sudden drop from about 35 fathoms, in a few
yards 50 fathoms giving no bottom. The angle, however, again
decreases, as off Afaga there is at least 600 yards between this
sounding and the 100 fathom line, which runs very evenly round
the whole island, including also the western islands. It in no
way curves in towards the cliffs, and hence I consider affords
strong presumptive evidence against any subsidence.
The passages in number and size are proportional to the
extent of the reef surface, and are the natural outfalls for the tide,
which probably keeps them open by its scour. At Noatau and
Lopta are perennial streams of fresh water, but there are no
passages especially attributable to them. The depth of the boat
channel varies, but does not exceed 2 fathoms. Between Husia,
a small island between Noatau and Afaga, and the main island are
depths of 10—11 feet, but the tidal currents set strongly there
and are gradually washing Husia away; off Malaha and by the
isthmus depths of 7—9 feet are not uncommon. To the north of
the isthmus is the deep pool of water, previously referred to,
which I consider to have been formed by the reef growing up
around,
At Noatau, Oimafa, Pepji and many places along the coast the
volcanic rock is shut off from the sea by the formation of a sand
flat, of which the isthmus also is formed. At Noatau it is about
500 yards broad and 1 foot above high tide level, rising for 2—3
feet higher near the beach. I dug into it in places to the depth
of 6—12 feet, but only found loose sand with fragments of corals
and nullipores. On the beach between tide marks it ends with a
beach sandstone formation in strata, 4—7 inches thick, dipping
down at an angle of 5°—10° to the sea. On the beach the ends of
6—7 layers may be seen. As these are removed the sand is
found to be less firmly consolidated, until in 3—4 feet it is quite
loose.
The top of a layer, which is the part most exposed to the air
and waves, is the hardest. If it is removed, as is constantly done
by the natives for gravestones, it seems to be rebuilt, growing up
as it were from the broken edge; fresh layers on the outside seem
to be formed too in a similar manner. These sand flats are very
444, Mr Gardiner, The Coral Reefs of [Mar. 7,
common in Fiji, and many show clearly the sandstone formation
on their outer sides; I have no doubt that many have been
formed by layer after layer of this rock being added to their outer
faces. It then a few feet back breaks down into sand, the rain
water perhaps, having plenty of carbonic acid gas in solution from
decaying organic matter, readily dissolving the finely divided
carbonate of lime by the deposition of which the sand was in the
first place consolidated. In the limestone islands m the Lau
group of Fiji the sandstone is much less broken down, some
recently dug wells in the flat showing the strata clearly; here,
however, the mud, caused by the wash of the sea on the limestone
cliffs, assists in binding the sand more closely, giving rise to a
much finer grained rock.
Mr Jukes, in his narrative of H. M.S. Fly's survey of the Great
Barrier Reef of Australia, has especially referred to this beach
sandstone formation. He in particular noted one island in the
Capricorn Group, where it was being washed away, probably
owing to a change of current from some reef growing up. After
dismissing the idea of elevation as a “difficult and gratuitous
hypothesis,” he suggests that “the present structure must have
been produced in the interior of a mass of loose sand by the
infiltration of sea or rain water, or some other cause of which we
are ignorant.” “After the interior of such a mass of sand had
been consolidated, the loose exterior may have been washed away
and the solid rock exposed.” In fact Jukes considered that this
rock is formed in the interior of a mass of sand, the formation
gradually proceeding outwards, while it seems to me patent that
it is rather formed on the outside and broken down within.
At Oinafa the sand flat has a height over most of its surface of
a few inches above high tide level, but 100 yards from the coast
opposite the anchorage there is a brackish swamp 1—3 feet below
this level about 800 yards long by 300 yards in greatest breadth
with in places pools 6 feet or more deep. On it more or less
buried in the sand are small blocks of coral strewn about, and a
crowbar cannot be forced down far without meeting the coral-rock,
so that the flat here appears to have been formed on the mner
edge of the reef.
From a consideration of the foregomg facts and the evidence,
collected at Rotuma, it appears to me probable that the reef has
been formed entirely at the present level. A gradual outgrowth
from the shore, due principally to nullipore growth, took place.
When it had reached a certain breadth, masses began to be added
to the rim, as at Funafuti, causing it to extend more rapidly.
A boat channel was then formed, partially by solution and partially
by the scour of the tide. As the whole broadened, this deepened
and sandstone flats were formed on its inner parts.
1898. ] Funafuti, Rotuma and Fi. 445
PART TI.
THE REEFS OF FIJI.
The Fijian Group has within its limits, as many observers
have pointed out, every variety of reef from the narrow fringing
to the well-formed atoll. Although there are many atolls in the
Lau, or Eastern Group, there is not one with any considerable
portion of its rim converted into land. To the east of the Ngele
Levu lagoon is a small island, divided by two channels into three
parts, but these are not more than 2 miles in length, while the reef
is over 40 miles in circumference and except for passages to the
south-west everywhere awash. The Nukusemanu and Nanuku
reefs in the Ringold islands are the north and south ends of an
atoll-reef over 80 miles in circumference, the greater part sub-
merged to a depth of 6—8 fathoms. Wailangilala is not properly
one of the islets of an atoll, being too high for such; it is, however,
formed of coral rock, and is probably the remains of an upheaved
coral island, the rest of which has been washed away. Other
atoll-reefs have only a few rocks but such are scattered on all
reefs, freely exposed to the seas, and are what I have before
called negroheads. These are especially abundant on the reefs
to the south-east of Viti Levu, and are simply masses of reef-rock
which have been torn from the outside and deposited in their
present positions, often several yards from the edge of the reef in
hurricanes, or other bad storms; some measure 6—8 feet in
height and must weigh many tons’. Barrier reefs too in Fiji have
no islets, a possible exception being Ono-i-lau, which has a number
of small islets to the east; two of these appear on the chart to
have.low hills and probably all are the remains of a larger island,
which has been washed away.
Another characteristic is the extreme regularity of the 100
fathom line round all reefs, freely exposed to the ocean. Off
prominent points it may be a little further out, but there are no
stretches of sea of any extent off the reefs with a less depth than
this; different atoll and barrier reefs, however near they may
lie to one another, are not connected by a less depth. The section
outside all is nearly the same, a gentle slope to about 40 fathoms
and then a sudden steep. There is further no essential difference
off those parts of Taviuni, which have no reef but the sea directly
washing their shores; the bottom here slopes to 40 fathoms in less
1 Capt. Wilson estimated that one, thrown up on the reef at Mbenga in the
hurricane of 1879, weighed 40 tons.
VOL. IX. PT. VIII. 36
446 Mr Gardiner, The Coral Reefs of [Mar. 7,
than 200 yards, and in the next cast-a few yards further out
I could obtain no soundings with 60 fathoms. Captain Wilson
pointed out to me that a ship can often get better anchorage to
windward than to leeward outside reefs, in other words that the
slope down to 40 fathoms is often more gentle to windward than
to leeward. This is distinctly so to the south-east of Taviuni,
where there is good anchorage, 300 yards outside the reef; south
of Cape Undu, to the north-east of Vanua Levu, I found that the
steep lay about 350 yards from the reef, while to the north it
began within 200.
The regular wind in the group for nine months sets from the
south-east to the east-south-east ; in the remaining months calms
and north to north-west winds occur. The current varies, being
largely affected by the wind, but from information, obtained from
skippers trading in the group, there seems to be always a definite
set to the west-north-west, which, however, with a wind from this
direction may be disguised by a merely superficial current in the
opposite direction. On an absolutely calm day the sea always
breaks on the windward reefs, while there may be no break on the
leeward, though the reef, as off Wakaya, is quite as high there.
The same phenomenon I observed too off the north-east point of
Vanua Levu, the reefs of the two sides of which I visited at
succeeding low tides without being able to appreciate any
difference in height; there was a distinct break for every wave at
high tide on the south-east reefs, but only one out of every five
waves broke on the northerly ones. Early in 1896 a timber ship
was wrecked on a reef off Vatoa to the south of the Lau Group;
some of the timber was recovered on the islands of this group,
but the greater part was washed to the south and east of Viti
Levu, showing a distinct current to the north-west.
Taviuni displays every type of reef from a mere fringe a few
yards wide to a well-formed barrier. The strength of the tide
through the Somosomo Strait varies up to 5 knots, the ebb flowing
to the north-east up by Rambi, while the flood sets along the
north end of Taviuni and to the south-west. Perhaps this strong
current together with a rather precipitous slope in places is
sufficient to account for the fact, that off a great part of this side
there are no reefs of any sort. From Wairiki to Wailanga there
is in places a hard platform extending out for about 50 yards,
above which the hills are usually separated from the sea by a sand
flat 50—100 yards broad. This platform is formed of reef-rock,
destitute even at its extreme outer edge, where it ends pre-
cipitously, of corals or nullipores. I believe that along this part
of the coast a broad fringing reef formerly existed, but after
growing outwards for some distance was checked by the current;
this gave time for the sand to accumulate, its wash finally killing
1898. ] Funafuti, Rotuma and Fri. 447
all the reef-forming organisms. Off this platform, after a sudden
drop to 3 fathoms, the slope is gradual to 40 fathoms, at which
the steep commences; the bottom is of sand, in most places
without masses or ridges. North of Taviuni 40 fathoms is often
reached in 100 yards, but then a flat commences with 40—50
fathoms and a breadth of 2—3 miles; its edge generally falls
abruptly, but there are traces of a barrier in some reefs almost
- awash with shallower soundings between. In the middle of the
strait is a small volcanic island, Koro Levu, which to the west and
south has a well-formed barrier but to the north-east a narrow
fringing reef; sheltered by it are a number of small isolated
patches. These reefs have all narrow, flat tops, covered with
icrusting nullipores and almost precipitous walls to 8 or 10
fathoms.
Off Vuna Point to the south-west of Taviuni a barrier reef
runs out for 2 miles, following the line of the coast, so that it is at
once suggested that it is formed on a bank piled up here by
the current through the strait; it is well protected too from the
east by a cape to the south, which is itself destitute of any reef.
The lagoon of this barrier has a depth of 10 fathoms and a sandy
bottom, the reef falling to it precipitously while the slope up to
the land is quite gradual. Off the south-east of Taviuni there is
usually some sort of a fringing reef, but only off Salia Levu is it
more than about 20 yards across, attaining here a breadth of
100—150 yards and having a well-defined rim, reef-flat and a boat
channel with a depth of 5—9 feet at low tide. The rim is com-
pletely covered with nullipores, and corals are rare both on the
reef-flat and in the boat channel, although the shore is strewn
with their branches. Outside the rim, which is similar in every
respect to that of Funafuti, masses almost as high extend for
some yards, the sea breaking on them; further out the bottom
is covered by masses and ridges with a fairly abundant, coral
growth.
The south-west of Viti Levu is fringed by a narrow reef,
unbroken practically save where the Singatoke flows into the sea.
To the east it is succeeded by a reef of the barrier class, which
extends up round the east coast, until it joins the Ovalau reef; it
nowhere lies more than 2—3 miles from the shore, and there are
large passages in it opposite the mouths of the Navua and Rewa
rivers and a small passage at Suva. The lagoon between Navua
and Suva is broken by a stretch of fringing reef, but on to the
Rewa river it is deep though often very narrow. The outer part
of the reef does not along this area differ materially from that of
Rotuma, but the channels inside the reef are practically devoid of
corals. The reef to the lagoon slopes steeply but not precipitously,
and by the land there is commonly a broad platform. The lagoon
36—2_
448 Mr Gardiner, The Coral Reefs of [ Mar. 7,
varies in depth up to 20 fathoms, having a bottom of dark grey
muddy sand with which the shore platform is also covered; in
many places too the reef has its breadth considerably increased
by the same deposit on its landward face, and shoals are covered
by it.
i The delta of the Rewa forms the whole south-east corner of
Viti Levu ; here the reef fringes and is as much as 3 miles broad.
This great breadth is apparently due to the sand with the earth
carried down by the river having filled up the lagoon. By the
island of Nukulau is the largest passage; it has a bottom free of
mud and. the bottom of the river too is for some distance clean
and hard, appearing to be formed of reef-rock. It seems to me
that the reef here formerly extended up under the delta of the
Rewa, and by the deposition of mud was gradually killed, growing
up afresh outside. The bottom is distinctly visible in the
Nukulau passage; it is by no means bare of corals and nullipores,
and has further a small reef awash in the middle. Yet the
fresh water and detritus of the river must have a considerable
effect or there should be patches and shoals of coral-rock in the
lagoon. :
Muddy sand is found on all the imner reefs and patches to the.
east of Viti Levu and the inner reefs of Ovalau are all coated by
it; that it forms often merely a thin layer over the reef-rock can
be plainly seen, but im many places it is undoubtedly filling up
the lagoon by its deposition. It varies largely in its composition
with its proximity to rivers and streams, but shells of Foraminifera,
fragments of Mollusca and Echinodermata, segments of such
algae as Halimeda and sponge spicules can usually be found.
It occurs further on all the imner reefs and some of the outer reefs
to the north of Viti Levu and Vanua Levu. Under water it sets
firm and hard, but does not apparently consolidate ; sponges and
green algae grow on it luxuriantly, but corals and incrusting
nullipores are never found.
Round the north of Viti Levu from Ovalau for some distance
there is a much broken barrier reef with one or two sandbanks,
like supplementary barriers between it and the shore, which
always has some sort of a platform. These inner barriers are
covered by the same muddy sand, which is of a lighter colour
owing to a less admixture of river washings. Thakau Moi, a shoal
to the north of Viti Levu, is a part of this barrier reef; its land-
ward side has a steep face, succeeded by a broad flat with a
central depression, which is covered by the same sand. The true
_ reef is a narrow strip on the outside, and it is only on the outer
face of this that corals, or reef-building nullipores, grow in any
luxuriance. I shall have occasion to refer again to this sand,
when noticing the raised reefs of Viti Levu; it enters largely into
1898. ] Funafuti, Rotuma and Fit. 449
the composition of some, and many have been, I believe, formed
‘by an analogous deposit.
The barrier reefs of Vanua Levu show all the characteristics of
the similar reefs elsewhere in Fiji, an abrupt rise from a sandy
lagoon, a reef-flat of variable breadth, raised rim with fissures not
generally very deep, a slope to 40 fathoms in 300 yards and then
the usual steep. Fringing reefs only occur to the south-east and
to the north of the entrance of Nateva Bay; they are fairly broad
with a distinct boat channel, devoid of corals. Nateva Bay has on
the west a broad shore reef covered with sand; outside is then a
clear stretch of water about 1300 yards broad bounded by a line of
reefs, on which corals grow in great luxuriance. The rest of the
bay is full of shoals and patches, on which also corals abound,
many seeming to have been formed by them alone. The Great
Barrier Reef of Fiji, extending through 24° of longitude, hes to
the north of Vanua Levu; to the west in the charts it seems to be
continued on by the fringing reefs of the Yasawas, but there is
really outside these a line of reefs and shoals, which connect it
round the west of Viti Levu to the fringing reefs of that island.
Off Waia the continuation is ill-defined; there is a broad flat
40 fathoms in depth studded with shoals-but soundings to the
outside show that a barrier is probably growing up. The small
island of Viwa alone stands outside the 100-fathom line of this
great reef; its rock is limestone, and it is probably a raised coral
island.
The Great Barrier Reef is in many places double, seeming to
consist of two reefs closely apposed, leaving only a narrow channel
between with 2—3 fathoms of water. In erossing it to the north-
west of Vanua Levu, we sailed through an outer reef about 200
yards broad into a channel of about the same breadth extending
‘as far as we could see with a sandy bottom; we then passed
through another reef into the lagoon. Both reefs near the passage
were covered with corals and nullipores and had flats falling
precipitously to the small channel between. The reef here is at a
considerable distance from the shore, and, while it is exposed to
the ocean to the north, it is beaten on its south side for the
greater part of the year by the waves of the trade wind; thus it is
quite conceivable that it should grow up with a face against both
and a lagoon between, since the growth of reefs everywhere seems
to be greatest, where exposed to the heaviest seas. The broad
lagoon within the Great Barrier Reef has an almost uniform depth
of 35—45 fathoms with a bottom of hard sand; it is studded with
patches and small: reefs, having precipitous walls to 20 fathoms
and summits almost awash at low tide. Near the land are a
number of larger reefs, some with depressions a few fathoms deep
in their centres and so somewhat simulating atoll-reefs. Thakau
450 Mr Gardiner, The Coral Reefs of [Mar. 7,
Levu’ off the west of Vanua Levu has a lagoon, 4—5 fathoms
deep, with a sandy bottom; the reef around is of sand except on
the extreme outer face where corals abound.
Between Viti Levu and Vanua Levu is a pool about 300 fathoms
deep with a sandy bottom. It has not yet been properly surveyed,
but my information leads me to believe, that there is against it on
all sides a much broken barrier reef. In it is a true atoll reef,
the Charybdis, with its eastern side awash at low tide, but to the
west much broken up by passages and deep channels. The current
runs strongly through the Vatu-ira Channel and then spreads out
in all directions while the usual direction of the wind is east-south-
east, so that it is those parts of the reef, which le to windward
and against the current, which have grown up.
To the south-east of the Vatu-ira Channel le a number of
volcanic islands, which resemble one another, with the exception
of Wakaya, in their hills sloping fairly evenly to the sea without
cliffs. Yet their reefs vary enormously ; they fringe or are barrier,
and have passages on all sides quite irrespective of the wind and
current. Mbatiki has a fringing reef, continuous except to the
north, where there are a large number of small patches; in it are
impounded pools of water 5 fathoms in depth. Round Matuka
the reef also fringes, but it has a well-marked boat channel with
2 fathoms of water, and is broken by two large passages to the
west and east, leading into pools of 25 fathoms. Moala has a
barrier 2 miles from the shore except to the north-west, where the
reef fringes; the lagoon has an even bottom at 20 fathoms. The
passages lie to the west, south-east and east (2) while the reef to
the north consists of a series of patches. Ngau has a fringing
reef except to the west and south-west, where there is a barrier,
enclosing a lagoon 30 fathoms deep and 3 miles across. The
fringing reef varies much in breadth and has a number of deep ~
fissures where the streams from the land flow. into the sea, while
the barrier has three passages to the north-west. South of Ngau
lies the Mumbolitha, an atoll-shaped reef with a shallow lagoon
and rim awash on all sides, very abundantly studded with negro-
heads. Nairai is completely surrounded by a barrier reef
enclosing a lagoon, 18 fathoms deep, with passages to the east,
west and north-west. 'Totoya is a crater, the south side of which
has apparently blown out. Its reef is a barrier having passages
to the north and west, and a small channel to the south; the
lagoon is 1 mile broad with a depth of 25 fathoms outside and 30
within the crater.
The reef of Wakaya is of the barrier class, distant 3—5 miles,
except to the south-west, where it fringes but has impounded
1 My information about this shoal is principally derived from native béche-de-
mer fishers.
1898. ] Funafuti, Rotwma and Fiji. 451
several pools of water, 5 fathoms deep, with precipitous walls.
The fringing reef is about 500 yards broad with no channel, but it
is full of holes up to 2 fathoms deep with their sides covered with
true corals, Millepora and Tubipora. I obtained from this part
in a few days more than 50 species of true corals of 21 genera,
and certainly both for variety and luxuriance of coral growth it
was the most prolific area I saw in Fiji. Outside this is a reef-
flat about 40 yards broad, covered with nullipores with a few
species of Pocillopora and Prionastrea; the rim is similar to that
of the Funafuti reef, but its fissures are not so deep. The barrier
reef is about 200 yards wide with but few corals; its passages lie
to the east and west. The depth of the lagoon varies up to 36
fathoms, but to the south depths of over 20 fathoms are rare and
the lagoon is much filled up by shoals with precipitous walls.
As if in correspondence with the reef, the island is bounded to the
west-south-west by precipitous cliffs, while the slope to the east
and north is similar to that of the volcanic islands to the south.
The north-west corner of the island is a sand-flat with a beach
sand rock, similar to that of Rotuma; on it are five lava hillocks,
each about 50 feet high and nearly all showing signs of wave-
action. To the east are also areas of beach sand, but off the whole
of this side lies an inner fringing reef, varying in breadth up to
200 yards and in places exhibiting almost the typical structure of
such a reef exposed to the ocean; corals, especially Millepora, are
very abundant on its outer face, which falls precipitously to a
sandy bottom with 5—6 fathoms of water, but incrusting nulli-
pores are not commonly found. To the north the barrier reef
joins on to that of Makongai, an island which slopes down evenly
on all sides from one main central peak. Its reef is of the barrier
class except to the east, where it is fringing, 900 yards broad with
pools of deep water, its lagoon is about 20 fathoms deep with
passages mainly to the north. Ten miles off the south end of
Wakaya lies the Horse-shoe Shoal, an atoll-reef with rim awash on
all sides except the north-west.
Most of the islands of the Lau Group are formed of limestone
and so the living reefs of this group are treated together with
their raised reefs. The island of Koro in the centre of the whole
group has steep hills and slopes; its reef to the east is of the
broad fringing type, but to the west is wanting. - Kandavu has a
well-marked barrier reef off its south-east, east and extreme north
sides, but off the rest of the island the reef is either wanting,
fringing, or represented by a few shoals. North-east of Kandavu
the North Astrolabe Reef is the barrier of an isolated rock about
10 feet high in its centre; the lagoon is about 14 miles broad but
only has a depth of 15 fathoms. There are two passages to the -
north, where the lagoon is fairly clear, while to the south it is full
452 Mr Gardiner, The Coral Reefs of [Mar. 7,
of patches and shoals. The barrier reef of Mbenga, including
four volcanic islands, is well marked to the south-east but much
broken to the north; this perhaps is accounted for by the strong
tidal current which sets through the passage between this island
and Viti Levu.
The mention of the foregoing facts is designed to point out the
great variability of the reefs in the Fiji Group and round even its
separate islands. It will further be evident that they bear little or
no relationship to the slope of the land, while the peculiarities of
some may be explained by the consideration of the currents and
winds prevalent in the group. The variability is so great indeed
that probably no single method of formation would explain all:
The further consideration, however, will be deferred to Part vi. —
PART IV.
THE RAISED REEFS OF FIJI.
SECTION I. Viti Levu.
The main branch of the Rewa river is fed by several streams
from the Kauvadra, a range of volcanic hills to the north of Vitu
Levu, which, rising from the coast of Viti Levu Bay, runs due
west for about 20 miles, whence it continues to the south with
spurs to the west, and divides the island into two halves. The
eastern half which is drained by the Rewa, has no long ranges of
hills, but is studded with isolated peaks, many of which are
characterised by having precipitous slopes and flat summits.
These are formed of limestone or of sandstone, in places obviously
overlying the volcanic rock, which is generally either a con-
solidated voleanic mud, or a vesicular lava. The hills above
Nailega on the Upper Rewa show clearly the characters of the
limestone hills, which reach their maximum height above sea-
level here; the sandstone resembles the limestone in its slopes,
and it is hard to find the one rock without the other near at hand.
The hill of Koro Mbasanga, as a type, has a flat summit, which on
three sides is bounded by cliffs of 150—250 feet; on the fourth
the slope is extremely steep for 100 feet, but then there is a
broad flat terrace to which succeeds a slope at about 70° for 200
feet. Below these cliffs the slopes are gradual except towards the
Rewa, to which the hill falls at an angle of about 30°; the height
above the river is about 700 feet, but, as the Rewa falls at least
200 feet below this, the total height is about 900 feet.
1898.] Funafuti, Rotuma and Fiji. 453
In the quarry at Suva two kinds of rock are found, a limestone
usually called coral-rock, and a sandstone to which the term
soapstone is locally applied. The coral-rock derives its name from
the presence of corals, many of genera still found living on the reefs
in the vicinity; shells of Echinoidea and Mollusca, principally
bivalves, are abundant, while sponges occur locally. The remains
of organic life, mentioned above, does not, I should consider,
exceed 10 per cent. of the total mass of the rock, the greater part
being of a coarse grained, friable nature, apparently formed by a
sand composed principally of rounded nodules and shells of Fora-
minifera. In places the remains of calcareous algae can be
recognised ; much of the rock, being of a very fine texture, round
and between masses of coral, implies from its position that it has
been formed by incrusting nullipores, as it has no appearance of
any organic origin, and loose sand is sometimes found underneath.
The rock then is a highly fossiliferous soft limestone. Between
Nailega and Soutoka on the Rewa crops out a dense, white, finely
crystalline limestone, closely resembling Carrara marble, only
harder. It is absolutely destitute of any trace of organic origin
to the unaided eye and its fractured surface has always the same
pure white colour. I received specimens too of a similar lime-
stone from some cliffs near the mouth of the Singatoke river.
The so-called soapstone is a fine grained sandy rock in which
the shells of Foraminifera are very common, and those of Lamelli-
branchiata can occasionally be found; its colour, when dry, varies
from light grey to pure white. According to Brady this rock
contains about 50 per cent. of silica, 18 per cent. of alumina, 3—8
per cent. of ferric oxide, 16 per cent. of water and traces ‘of
potassium carbonate, etc. When first exposed in the quarry, it
has almost a blue lustre; then, as it dries, it gets a soapy feel,
and finally can be seen to be a very fine grained, friable, sandy
rock. “ Where it is covered by the water in the beds of streams, it
remains hard and firm, but by the banks there is a tendency for
-its surface to flake off.
From Viti Levu Bay to Navatu on the Rewa the rock is all
soapstone, but below this village there is an outcrop of volcanic
rock which it overlies. By the village of Nailega, lower down,
both soft limestone and soapstone rocks are found, the former
resting on the latter. Then the banks of the river show soapstone
overlying the crystalline limestone, of which there is a small out-
crop on the right bank. A volcanic conglomerate is next found, |
to be succeeded on the right bank by several low lying hills,
formed apparently entirely of crystalline limestone. From this
point soft limestone and soapstone rocks alone occur down to the
delta of the Rewa.
1 Note on the so-called ‘‘ Soapstone of Fiji.” Quart. Jowr. Geo. Soc. Feb. 1888.
454 Mr Gardiner, The Coral Reefs of [ Mar. 7,
In the quarry at Suva, which runs into the edge of a cliff,
there is in the section exposed about 2 feet of earth on the top of
a layer of soapstone, 6—10 feet thick, while it is nearer 30 feet
in most parts of the cliff. The line of junction of the soapstone
with the coral-rock below it is horizontal, and along this lme
there is a layer about an inch thick of unconsolidated sand; in
the soapstone it is immediately above this layer that most bivalve
shells are found. The coral-rock is about 65 feet thick on the
face of the cliff. Its upper few feet are very granular, being
formed of small nodules and sand, with few corals or shells.
Twenty feet below at the bottom of the quarry it is much coarser
on account of numerous fossil shells and corals. Vertical fissures
a few inches across run in from the edge of the cliffs; their sides
are coated with crystalline carbonate of lime. Under the coral-
rock the soapstone is again found and extends into the sea, its
thickness being at least 150 feet. On top of it is a layer of
pebbles, varying from 1 to 2 feet in thickness, formed both of
soapstone and of a volcanic conglomerate; in size they vary, many
being several inches across. Fragments of coral, some apparently
water-worn, are found in the same layer, and bivalve shells are
more abundant than in any part of the coral-rock above.
The village of Kalamba about 6 miles from Suva is situated
on the flat round top of an almost precipitous hill, rising suddenly
to a height of 220 feet. Round one side a tributary of the
Tamavua river flows, and to join this a small stream has cut itself
a tunnel through the hill; this is about 250 yards long and
70—100 feet high with a fall of about 60 feet. The rock exposed
in the section can be seen to be very distinctly stratified hori-
zontally, and I distinguished the following layers :—
1. Earth about 2 feet.
Soapstone ,, 60 _,,
Coral-rock ,, 50 __,,
Soapstone ,, 30 _,,
Sand Tai) ae
Coral-rock ,, 12 _,,
Soapstone ,, 75 ,,
8. Black vesicular lava in the bed of the larger stream.
MTD OC wm gH bo
The soapstone, in all its layers, has its typical appearance but the
two layers of coral-rock are very different. The upper is coarsely
grained, plentifully strewn with pebbles of soapstone, bivalve
shells and sponges but with no corals; its upper 10 feet almost
form a distinct shell layer. The fifth layer is a very fine pebbly ~
rock with red and black volcanic nodules. Corals are plentiful in
the sixth layer, which closely resembles the coral-rock of the
1898.] Funafuti, Rotuma and Fiji. 455
Suva quarry but has fewer shells; a distinct pebbly layer forms
its lower foot, and separates it from the soapstone, which is of a
much finer grain than either of its upper layers. The lava also
forms the greater part of a hill on the opposite side of the stream,
where it distinctly overlies the soapstone, and is as distinctly
overlain by it.
The soapstone nowhere shows any great variations, whereas
the coral-rock in places by the Rewa consists mainly of corals and
sand; I nowhere found it as a hard firm rock like that of a
growing reef, although it is much harder on its outer face, where
exposed to the weather. In some parts it consists of masses of
almost structureless, fine grained rock, which sometimes le in
layers. Large and deep caves and small cavities are very common
in it’. The greatest thickness near Suva is about 80 feet, but by
the Rewa I found beds of at least 200 feet. I have no doubt
whatever that this coral-rock was formed in the same way as
coral reefs are now being formed; its great variability I consider
to be due to the different positions with regard to exposure to the
ocean, in which its reefs were built up.
Of the soapstone Brady examined specimens from the shore
road, from an elevation of 100 feet or more and from an inter-
mediate point at Suva. He found that they varied considerably
in their species of Foraminifera, specimens from the first and
second localities having only 36 species in common out of 92
obtained in all; he also found the remains of a few Ostracoda,
but did not apparently obtain any bivalve Mollusca. Of the
Foraminifera, Brady points out that 87 species still live in the
neighbouring Pacific, the other 5 being very rare. Comparing
the species from this rock with lists from material, collected by
the Challenger Expedition, Brady remarks that “it is found to
include several forms, not recorded from depths of less than 129
fathoms, and certain others, of which the minimum depth is about
150 fathoms.” He then concludes :—‘ Nevertheless judging from
its general facies the Rhizopod fauna is one that I should expect
to find in a deposit forming from 150 to 200 fathoms (rather more
than less) in the neighbourhood of any of the volcanic islands of
the Pacific.”
Should Brady be right there would be an almost incompre-
hensible series of elevations and subsidences required to form
such a hill as Kalamba, unless the coral-rock be also supposed
to have formed at depths of 150 to 200 fathoms. I do not assert
that this is impossible, but such evidence as there is points to its
being exceedingly unlikely, and, if so, there should certainly be
1 Capt. Langdale, late R.N., informed me that up the Wai Mala branch of the
Rewa there is a large hill, formed entirely of this rock, which is pierced through by
several ramifying tunnels.
456 Mr Gardiner, The Coral Reefs of [Mar. 7,
the remains 1n it of the rest of the fauna of this depth. The inner
reefs, described with the living reefs, are round the large islands
coated with a fine muddy sand, in which the shells of many species
of Foraminifera occur. I would suggest that the soapstone really
had a similar origin, and that it is a shallow water deposit; on
these reefs few. Mollusca, Echinodermata and other animals and
plants are found, such as might be supposed to leave traces of
their origin. The deposition of this muddy sand can be at no
time very rapid, as it depends largely on the amount of earth
carried down by the rivers. The surface is hard and firm, so that
trees and other vegetable matter from the land would not
ordinarily have time to get imbedded before they decomposed or
were destroyed.
The formation of such a soapstone at 200 fathoms is quite
possible; in this case it should form flat banks 1—2 miles wide
opposite the rivers, which carry down to it its silica and alumina.
It is quite inconceivable, when one considers the rugged nature of
the soapstone country of Viti Levu, how it could have been formed
from these flats. There would indeed require to have been a
whole series of elevations over small areas close to one another,
since it is quite impossible to ascribe the forms of most of the
hills to rain and river action alone. These inner reefs on-the
other hand have steep slopes, vary enormously in size, and are
distributed over all the lagoons within the barriers of Viti Levu
and Vanua Levu; the distribution of living corals varies, and is
often completely changed over large areas owing to local changes of
current. I think the section of the raised reef at Suva shows how
it has itself been formed. There was a sandy reef at first near the
mouth of some river or stream, when owing to some small change
in current pebbles began to be deposited. These pebbles of course
gave a firm foundation for the coral larvae, and a reef began to
grow up; but, before this reef reached the surface, a deposit of
sand on it, possibly from another change of current, killed the
corals, and then a further deposit of muddy sand took place on its
surface, perhaps raising it almost to the sea-level, before it was
upheaved to its present height.
The crystalline limestone does not form any ranges of hills,
sufficiently large for any theory of a coral reef origin to be put
forward. It is overlain by the soapstone, and was more probably
formed from a chalk, which by the infiltration of water has meta-
morphosed.
1898.] Funafuti, Rotuma and Fiji. 457
SECTION II.
Tue Lav Group.
The Lau, or Eastern Group of Fiji, consists of a line of islands
and atoll-reefs, extending from lat. 16° 30” S. to lat. 21° S. with a
breadth of about 1° of longitude; the line is continued 1° north-
wards by the Ringold islands, and properly includes Thikombia-i-ra
as well. Of reefs, every description is to be found from the narrow
fringing to the perfect atoll-shaped.
The islands may be divided into three classes in accordance
-with the rock of which they are formed :—
1. Limestone.
2. Limestone and volcanic.
3. Volcanic.
Even at a considerable distance, it is possible with almost
absolute certainty to say whether the rock is volcanic or limestone.
The vegetation of the former consists of coarse grass, reeds and
small bushes; the hills are usually conical, the gradients easy, and
at the base there is invariably a more or less extensive flat. The
limestone on the other hand is densely covered with heavy timber,
grass and reed being absent owing to a lack of surface soil; the
hills are flat-topped with precipitous slopes, which end seawards in
overhanging cliffs, appearing extremely white, where recent falls
_of rock having taken place, against a light grey ground colour.
1. Limestone Islands.
To the south Fulanga (Fig. 6) presents an almost complete ring
of land, surrounding a central lagoon; its diameter is about
5 miles in a north-west to south-east direction, and at right angles
to this 4. The ring is complete except to the north-east, where
for 3 miles it is broken up into separate islands between which a
coral reef extends except for a ship’s channel, about 34 cables
long, 60 yards broad and 6 fathoms deep with a tidal current of
about 5 knots. The land varies from a few hundred yards to
a mile in width to the south-west with an average breadth of
about 800 yards. The enclosed lagoon, 34 by 2 miles, has a
depth of 5—6 fathoms, but to the north-west 10 fathoms are
found. It is studded with rocks and islets varying in height up
to 100 feet, a distinct row extending right across to the south
of the ship’s entrance. The above ring of land is very uniform in
elevation, ending precipitously at either end where the break
occurs; its general height is about 210 feet, but Quoin Hill to the
458 Mr Gardiner, The Coral Reefs of [Mar. 7,
north is 260 feet, and to the south-west are two hills 240 feet
high. There are, however, three or four narrow gaps with
precipitous sides from 30—50 feet below the general level of the
ridge.
FULANGA
Fig. 6.
Towards the lagoon the rock ends in low, overhanging cliffs,
except in the bays, which generally have sandy beaches. From
these the land rises gradually for some distance, followed by an
almost precipitous cliff 30—40 feet high, reaching to the summit
of the ridge, where there is a flat plateau, which varies extremely
in width, in some places being at least 250 yards broad, but im
general little more than 100; beyond this, towards the ocean,
there is usually an almost precipitous fall. The north side of
Quoin Hill is a precipice 260 feet high, with a sea-washed base ;
the shore too along the whole of the north side is very similar. To
the south-south-west the fall is about 80° generally; outside this
there is an extensive sand flat, upwards of 400 yards broad. This
flat is composed of a very fine grained, almost muddy, white sand,
consisting of the remains of Foraminifera and calcareous algae,
especially of the genus Halimeda, but mainly of the limestone
very finely pulverised. It is about 4 feet above high-water level,
and wells, after passing through the beach sand rock, reach in
8 feet what appears to be the reef-rock ; their water is brackish,
percolating through from the sea.
In the limestone are occasionally large crevices several feet
egy d aonf of ‘XI “TOA ‘QG8T “90S “7M “00Ng
1898.) Funafuti, Rotuma and Fiji. 459
across, with caves here and there and numbers of small tunnels.
Where the rock is weathered, it is grey, rough, sharp and much
pitted, while its fracture is white, not uncommonly streaked
with red; the appearance presents no trace of organic structure.
When broken into, holes are often found, a few inches to some feet
in diameter, having rough and rugged sides; other parts show
pockets of a red hard amorphous sandy rock, apparently very
largely consisting of ferric oxide. Low down, especially where
directly acted upon by the tide and spray, the rock is much more
crystalline, its rough projections being frequently entirely formed
of transparent, yellow, prismatic needles, or shorter and thicker
crystals.
Where .exposed to the action of the waves, the rock is worn
away to an extraordinary extent, so that many of the rocks in
the lagoon are mushroom-shaped. The height at the edge above
low water is from 7—15 feet, depending largely on the waves and
hence on the exposure, the stretch of water that the wind may
have for raismg a sea. On the seaward face of the island it is
generally low, as much wave action is impossible, owing to the
reef breaking the waves; within the lagoon near the passage it is
greatest. The cliffs by the sand flat to the south-west have the
same undermining, proving that it was formed by the sea piling up
the sand. In the lagoon there is usually a flat platform at low
tide level, running from the base of the cliff to the outer edge of
the overhanging part, where it drops directly into 2 or 3 fathoms
of water; on its surface are a few calcareous algae, a little weed
and some worm tubes. The heads of these mushroom-shaped
rocks in the lagoon are often very evenly convex; occasionally one
can be seen by the wearing away of its stem to have fallen over
to one side. Not uncommonly large masses have split off from
the sides, and south of the entrance is one which has broken into
two across the middle. The portion of the platform, which should
have been covered by these split-off masses, is not, unless the fall
is very recent, visible and must have been washed or dissolved
away. Every stage from a well-formed islet to a small patch
2—3 fathoms deep can be seen; no shoals appear to exist, which
cannot be ascribed to the solution of these islets. Within the
lagoon no corals and no reef-forming nullipores live, the bottom
consisting of a fine, soft, white, sandy mud, the deposit of which
on any coral would quickly prove fatal; solution is going on con-
tinually and there is no balancing growth. The final result should
be a perfect atoll-reef just awash, the land being dissolved away
while the living reef round it continues to grow. (Plate.)
The whole island is surrounded by a fringing reef, off Quoin
Hill very narrow, but to the south-west half-a-mile broad with
a well-marked channel, 2 fathoms deep; to the north-east it
460 Mr. Gardiner, The Coral Reefs of [Mar. 7,
extends between the islands, except at the ship’s passage, and is
very broad. At low tide a few boulders can be seen on the outer
edge, especially off the north of the island; all are small, and.
could have been thrown up, as they doubtlessly were, by strong
gales. The 100 fathom line is extremely close to the reef, follow-
ing the contour of the land; on the north and south it is noticeably
nearer than to the east and west, being off Quoin Hill almost
contiguous with the outer edge of the reef.
About 5 miles to the east of Fulanga lie the reefs surrounding
the two islands, Ongea Levu to the north and Ongea Ndriki to
the south, Both in the nature of their rock are of a similar
character to Fulanga and resemble it further im each having
a small lagoon. Ongea Levu is 4 miles long by 2 broad, lymg
almost north and south; it is surrounded by a ridge with
precipitous overhanging cliffs on the outward side, which are not
generally as high as those of Fulanga. Southward this range is
broken, where the water of the lagoonlet joins with that of the
lagoon of the barrier reef; a number of islets, however, in two
lines join it across, and make the ring complete. These latter
range up to about 80 feet, while the ridge is about 200 feet high
with a hill northwards of 270 feet. These rocks across the entrance
of the lagoonlet present the same characters as those within the
lagoon at Fulanga; one shows at low tide an arch in the centre,
where the middle has been washed away. Near these the lagoon-
let is about 5 fathoms deep, but northwards it gradually shoals,
uncovering at low tide a reef about 200 yards across; this merges
into a sand flat, from which the land rises to the ridge, as at F ulanga.
Ongea Ndriki resembles the last island, except that it is
smaller, more circular in shape and rather higher; the ridge
is open northwards, opposite the break in that of Ongea Levu.
These breaks in the ridges of the two islands are so strongly
joined by isolated rocks, and the ridges themselves bend so
markedly towards them, that the two islands seem always to have
been completely separated.
South of Ongea Ndriki the reef fringes, while it contains on
the other sides, as a barrier round the two islands, distant 1—2
miles; it has four passages, one to the north and three to the west
opposite the channel between the two islands. The depth of the
lagoon is from 4 fathoms between the islands to 13 fathoms out-
side them, with a bottom of fine muddy sand and few shoals; the
depth of the largest western passage is 13 fathoms and the
strength of the tide through it is 2—3 knots. The water was ver ry
distinctly milky at the ebb tide, forming a well-defined streak in
the sea outside. North-east of the barrier is a small reef, Thakau
Teteika, a few hundred yards away, with a channel between of
over 100 fathoms.
1898.] Funafuti, Rotuma and Fin. 461
Namuka, 14 miles north-by-west of Fulanga, is about 4 miles
long by 14 broad, its long axis lying east and west. A ridge with
cliffs to the sea surrounds it; the heights are, as registered, 260,
240 and 210 feet; otherwise it is very even, but its plateau seems
to be much narrower than at Fulanga. To the south is a small
lagoonlet, 1 mile broad with a sand flat at its head; the ridge, as
in the last islands, is continued across its entrance by isolated
rocks. The land at the ends of the island within the circle of the
ridge is from 50—100 feet above the sea-level ; it has no appear-
ance of a deep valley, but the ridge rises from it with more
precipitous and higher cliffs than at Fulanga. The rock is the
same kind of limestone, by the lagoonlet being remarkably hard
and crystalline with numerous pockets of the red sandy rock.
Numerous large caves are found on the outer face of the island,
and seemed to be situated in horizontal lines along the cliffs.
The reef is barrier about 1 mile distant from the shore, but to the
east fringes, and off the north-west consists of isolated patches,
covered with reef-building nullipores and corals; the lagoon is
7—14 fathoms deep.
The Yangasa Group lie south-east of Namuka and consist of
four islands in the lagoon of a barrier reef, 22 miles in circum-
ference, having a passage on the north-west side. They are
stated in the survey to be of coral, and this is corroborated by the
appearance of their slopes and vegetation. The natives also have
the same name for the rock, and state that it overhangs on all
sides, making landing very difficult. Yangasa Levu, the largest
island, seemed from the ship to have two flat summits; on the
sides of these, running across the island, are two terraces, the
slope between being about 70°. The other islands of the group
are 210, 240 and 270 feet in height.
About 14 miles east of Namuka, Wangava, a long, narrow
island lying north-east to south-west, 3} by 1 mile broad, is
surrounded on all sides by steep cliffs to the sea and has an ex-
treme height of 350 feet. The ridge round the island with the
exception of this hill is almost of a uniform height of 260 feet
with few undulations. To the centre its slopes are extremely
abrupt, and in it in reply to careful inquiries the natives stated
that there is a lake in which the tide regularly ebbs and flows’.
There is no doubt that its rock is all of the same limestone, the
fracture showing clearly in one place white and its cliffs over-
hanging very conspicuously. Round the island is a narrow
fringing reef, which north-west only consists of isolated heads and
patches.
North-west of Wangava at a distance of about 35 miles lies
1 I am indebted to the Hon. L. Allardyce, Native Commissioner, for these and
numerous other inquiries. :
VOL. IX. PT. VIII. 37
4.62 Mr Gardiner, The Coral Reefs of [Mar. 7,
Vanua Vatu, a saucer-shaped island 14 miles in diameter with
steep cliffs all round; its height is 310 feet, and it appears
regularly table-topped from the sea’. Its reef fringes except to
the north-west, where it is of the barrier class.
Naiau, Tuvutha, Mango, Vatu Vara and Naitamba have all
table-tops and the characteristic appearance of limestone islands;
they are respectively 580, 800, 607, 1030 and 610 feet high.
Vatu Vara has merely one flat-topped peak, but the others are
typically round with central depressions about 200 feet below the
ridge. I was informed by Capt. Wilson and Mr Chalmers, a
former magistrate of Lau, that all are formed entirely of lime-
stone; this is confirmed by the survey? and very fully by their
appearance from the sea. In the interior of Mango nodules of
manganese are stated to be common, and, to drain it, a stream has
cut itself a passage to the outer side through the ridge. The
other islands are all said to have water holes in the centre, in
some of which the water is salt, though not below sea-level.
From the sea all appear to have very steeply sloping or pre-
cipitous cliffs, and I could see no trace anywhere of volcanic soil
or rock; terraces are nowhere visible. The reefs usually are
fringing or very slightly barrier; off Mango the reef has a few
low islets. Vatu Vara alone has a considerable stretch of low
lying land by the shore, rising gradually for 250—300 feet above
the sea and then precipitously for the last 700 feet ; southward its
hill ends in a cliff over 900 feet high.
Thikombia-i-ra is, to judge from the descriptions I have
received and its appearance, certainly of limestone. Capt. Wilson
also told me that the rock is precisely the same as that of Fulanga,
and that at one of the chief landing-places a ladder is let down
through a hole in the overhanging cliff to ascend by. Its greatest
height is 680 feet, but it has several summits and no ridge; its
hills at a distance appear to be very distinctly terraced. There is
no living reef of any sort except to the east-south-east, where a
barrier extends out for about 2 miles. The 100 fathom line lies,
however, about 13 miles beyond the reef, and there is a large
plateau 45 fathoms deep; the edges in places are considerably less
deep, and it is in all probability an upgrowing barrier reef.
Of the smaller islands in Lau, most are of the same hard
limestone, but a few low lying ones seemed to be formed of a
soft limestone, in all respects similar to the ordinary reef-rock.
Vatoa, I was informed, has both kinds of rock; its reef is both
barrier and fringing, the former with in places a deep lagoon.
1 Captain Wilson informed me that, near the landing place, the rock is much
indurated with large clam shells (Tridacna ?)
2 Vide Sailing Directions for the Fiji Islands, 1882,
1898. ] Funafuti, Rotuma and Frye. 463
2. Limestone and Volcanic Islands.
Chief in this class for interest is Kambara (Fig. 7), an oval-
shaped island, close to Wangava, lying north and south, with a
length of 44 and a breadth of 3 miles. The island is. bounded by
precipitous cliffs on all sides except to the west, where there is
a hill, 470 feet high, known as Delai Yaloi. Into the middle of
this hill the cliffs surrounding the whole island run. Towards the
sea its slope is very steep, up to 45°, but it is nowhere precipitous;
it slopes too similarly along the sides of the cliffs and towards the
centre of the island. The cliffs around the island average 250 feet
in height, but to the east there are two eminences of 320 and
300 feet. By Delai Yaloi the elevations are somewhat lower; and
220
of °
oi) we
< = >=
WES
“Rg Mae
Scale “XxX ee ee
0 l aR age
Miles 60077
KAMBARA
Fig. 7.
the cliffs, north and south, are separated from the sea by a sand
flat, otherwise they continue evenly round the whole island. This
hill is thus 150 feet higher than any other point on the island
and about 230 feet above the cliffs near it. Its rock is a dense
basalt, which has apparently welled out from a fissure near the
base of the limestone cliffs, and gradually increased in height, so
as finally to overflow them and form a high hill. Near it, and
especially where its rock overlies, the limestone is dense and white
with a less tendency to form chasms, pits and caves than is usual ;
it is also not nearly so hard and crystalline, and preserves traces |
of its organic origin. Elsewhere the limestone is similar to that of
Fulanga, but perhaps a little denser. On the surface of Delai
37—2
464 Mr Gardiner, The Coral Reefs of [Mar. 7,
Yaloi large limestone blocks are found strewn about, as if carried
up by the eruption which formed it. On the ascents there are no
sea shells, nor sea deposit of any sort; indeed, this hill must have
been formed, not only subsequent to the formation of the lime-
stone, but also to its upheaval. It could not have been formed
simultaneously with the upheaval, or the precipitous limestone
cliffs, cut off by its lower slopes from the sea, would have had no
existence.
From the cliffs the land slopes in everywhere gradually towards
the centre of the island, which forms a broad plateau about 100
feet above the sea. The slope is, however, sometimes uneven,
forming precipices 20—30 feet high. On the plateau itself are ~
many small hills, rismg nearly to the level of the rim, with very
steep walls, and some springing out almost like buttresses from
the rim itself. The natives affirm that in this plateau there are a
number of deep holes, in which salt water is found and _ tidal
influences are felt. The rim is somewhat broken as if by dykes
40—100 yards across; its breadth varies greatly, but generally
the ridge is at least 100 yards across.
Round the whole island the reef is fringing and narrow with
a channel, 1—2 fathoms deep, for some distance to the south-west
of Delai Yaloi; north-west of this hill and off it, it is merely
represented by a few sunken patches growing up’.
Vanua Mbalavu, the largest island of the Exploring Group (Fig.
8), is of mixed origin. Within the barrier reef, enclosing the group,
islands of all the three kinds are met with; of these Thikombia-1-
lau, Sovu, Avea and Munia stand quite apart, while Susia and
Malatta really continue the main island to the south and east, the
three being surrounded by the same inner fringing reef. Thi-
kombia-i-lau standing 550 feet, Sovu 230 feet, Avea 600 feet, and
Malatta 420 feet high, are all of the same dense limestone as
Fulanga, while Munia, 950 feet high, consists entirely of erupted
rock. Susui, 430 feet high, to the east of Malatta, has its west end
of limestone much undermined by the sea with precipitous cliffs ;
to the east this passes gradually into volcanic rock with more
gentle slopes.
Opposite Avea on Vanua Mbulavu is a hill, Koro Mbasanga,
930 feet high. From this the island runs west for 6 miles and
south for 8, its average breadth being about 2 miles. North-west
at the base of Koro Mbasanga is a deep creek, the rock of which
on the west side is limestone, precipitous and much undermined,
while on the other side the shore is formed by the slopes of this
hill, the rock of which is volcanic. The two rocks join here with
no sharp line of demarkation except in the vegetation, the lime-
1 The reef in Fig. 7, which is taken from the chart, is not quite accurately
represented.
1898.] Funafuti, Rotuma and Fiji. 465
Thikombia i lau PN
550) s L
reg
eee
BiG 8.
EXPLORING GROUP.
466 Mr Gardiner, The Coral Reefs of [Mar. 7,
stone running straight into the volcanic rock, and being covered
by it in many places. In fact it would seem as if Koro Mbasanga
had been formed subsequent to the elevation of the limestone in
precisely the same way as the volcanic hill at Kambara. To the
west the island is all limestone, much cut into by creeks and
broken up into isolated hills, forming an irregular range in the
centre, with peaks and buttresses on either side, ending in cliffs
seawards with heights up to 600 feet. ‘To the south the land is
undulating, having down its centre a ridge, steep but not pre-
cipitous; to the east is an extensive sand flat by the shore. This
volcanic rock is a friable and very crystalline conglomerate, break-
ing down into a red coloured earth. About a mile from the south
end limestone again recurs; it 1s here exceedingly crystalline and
much coloured by oxide of iron. At the juncture of the two rocks
are some hot springs, in one of which the water is nearly boiling.
Here again the limestone appears to have been formed before the
eruption of the voleanic rock. The cliffs, however, are not especi-
ally precipitous, nor is the amount of water action so great as
to lead to the conclusion that so much time had elapsed between
the elevation of the limestone and the eruption of the volcanic
rock as at Kambara.
The barrier reef of the whole Exploring Group (Fig. 8) is about
80 miles round, lying far distant to the east, but to some extent
fringing Munia, Susui and Malatta. Within it round Vanua
Mbalavu is a fringing reef, small and inconspicuous off the lime-
stone part, projecting indeed little beyond the distance to which
this rock overhangs. The general depth of the lagoon is about
35 fathoms, with a pool in the centre about 75 fathoms deep; shoals
and patches abound in the shallower parts. The passages for such
a large lagoon are exceedingly few and small, but all have depths of
over 10 fathoms, and around the eastern one the 100 fathom line
runs for three miles into the lagoon; the other passages are one to
the south, one north-west, and two north, near the island of Sovu.
Lakemba has flat limestone hills, rising abruptly to a height of
60—70 feet on the west coast, the foundation being the volcanic
conglomerate, which forms the rest of the island. I was informed
by the Rev. C. Heighway, resident missionary, that these are
frequent round the whole island, and that inland there is generally
a small flat at their base; they should then represent an upheaved
barrier reef. Inside these the island trends gradually upwards to
two peaks in the centre about 700 feet high; there are good
springs of water and deep water-courses. The reef is fringing off
the west side, but a distant barrier off the east.
One to the extreme south, Capt. Wilson stated, has some of the
islets coral and some volcanic. He considered the three larger
islands in the centre to be the remains of an old crater.
1898. ]} Funafuti, Rotuma and Fijt. 467
3. Volcanic Islands.
The rock of these islands is usually a dense, coarse, and heavy
volcanic conglomerate with no vesicular lava and no remains of
craters. Most of them have well-defined water-courses, broad
fringing reefs and often distant barrier reefs as well. There
are no signs of recent activity or movement.
Mothe, to the south, rises to a single peak of 590 feet, and has
a considerable barrier reef round it with a long extension south-
wards. In the same lagoon is a small island, Karoni, 120 feet
high, the formation of which is doubtful; as seen from the ship
it appeared to be of limestone.
Thithia, 540 feet high, is a larger and rounder island with
several peaks of about the same height, fringed by a broad reef.
Kanathea has several peaks up to 330 feet, with an extensive
barrier reef. Yathata has a single conical hill of 840 feet, with a
broad fringing reef.
SECTION III.
SUMMARY AND CONCLUSIONS.
Considering the peculiar forms that these islands of limestone
and of mixed rock in the Lau Group take, it is impossible to
conceive that they can have had any origin different to that
of many of the atolls, barrier and fringing reefs of the present
day. They differ however in the great hardness and dense nature
of their limestone, and that it shows little or no signs of organic
structure. I have already given my reasons for considering that
the soft limestone of the eastern half of Viti Levu had its origin
in coral reefs, which, although some may have been inner reefs,
cannot have differed essentially from the reefs, which formed the
Lau Group. The surface of these soft limestone reefs where it is
exposed to the atmosphere is no doubt harder than the interior,
but metamorphosis has only taken place in the small fissures, where
the carbonate of lime has obviously been dissolved by the carbonic
acid gas in solution in the rain water and been redeposited.
The raised reefs of Tonga!, the Solomon Islands, and Cuba’,
seem to be formed of absolutely similar limestone. From the
character of these reefs, together with those of Fiji, I can scarcely
1 The Geology of the Tonga Islands, by J. J. Lister. Quar. Jour. Geo. Soc. 1891.
2 The Geology of the Solomon Islands, by H. B. Guppy.
3 On the elevated Coral Reefs of Cuba, by W. O. Crosby. Proc. Boston Soc. of
Nat. Hist. xxur. 1882—3.
468 Mr Gardiner, The Coral Reefs of [Mar. 7,
believe that the metamorphosis from the heap of organically
deposited material, like the reef of the present day, can have
been subaqueous. Neither do I believe that the change has been
to any great extent effected by the interfiltration from the sea
of carbonate of lime in solution. The deposition of finely divided
carbonate of lime would, of course, greatly tend to fill up the
pores of any coral, but this is not an interfiltration. The cavities
in the hard limestone can be accounted for by the shrinkage that
would naturally occur in its metamorphosis; I have also already
shown, in my description of the reef at Funafuti, that in the
erowth of a living reef spaces are often enclosed. The pockets of
oxide of iron are due to the solution and abrasion of much of the
rock by the rain during its metamorphosis, when it would of
course be left undissolved; the higher lying rock is much freer
from it than the lower, as should in such circumstances be the
case. The rock at Kambara, covered by the lava, is almost
intermediate between the soft limestone of Suva and this hard
limestone. The beach sand rock of Rotuma, a white, loosely
compacted limestone, is, as I have pointed out, used by the natives
for gravestones, becoming on exposure exceedingly hard and com-
pact, the various constituents being cemented together by calcite.
I believe that im these small slabs a metamorphosis is now taking
place precisely similar to that which has formed the dense highly
crystalline limestone of the Lau Group out of the loosely aggre-
gated masses, such as form a coral reef at the present day.
I am greatly indebted to Dr Pollard, of the Caius College
Laboratory, for having kindly analysed two specimens of this hard
limestone. Both came from the inner side of the ridge of Namuka,
the one being a pure white rock without any large crystals, and
the other a very fine grained reddish rock. The white rock (two
determinations) gave 78°6 per cent. carbonate of lime and 21°5
carbonate of magnesium. The red rock gave 85:2 per cent.
carbonate of lime, 6°7 carbonate of magnesium, 4°2 oxides of iron
and aluminium, and 3°5 silica}.
These analyses show that dolomitization has gone on to a
considerable extent in this hard limestone. Dana states? that
95—98 per cent. of the common reef-corals is formed of carbonate
of lime, the remainder being made up of 14—4 per cent. of organic
matter with about 1 per cent. of earthy ingredients. Dana also
notes* that coral sand and mud contain little or no magnesia
generally; he gives however an instance where 1°38 per cent. was
obtained. These analyses, so far as they go, afford no probability
1 Analyses of two very white specimens from Kambara and Fulanga gave me
19°8 and 10-7 per cent. respectively of carbonate of magnesium.
2 Coral and Coral Islands. J.D. Dana, 1890, p. 99.
3 Loe. cit. p. 394.
1898.] Funafuti, Rotuma and Fiji. 469
of the dolomitization having taken place under water with the
reef im situ. Abrasion from climatic causes has certainly gone on
to a very large extent. The rain water takes up a certain amount
of carbonic acid gas, when exposed to the air, and by means
of this acts on the limestone, dissolving its carbonates of calcium
and magnesium. There can be no doubt that this is due to a
chemical compound being formed, and I would suggest that a
certain amount of pure calcium magnesium carbonate {MgCa(COs)o}
is always formed at the same time and deposited on the evapora-
tion of the water. One litre of water saturated with carbonic
acid gas under atmospheric pressure dissolves ‘31 gram of calcium
magnesium carbonate at 18° C., ‘88 gram of calcium carbonate at
10° C., and 1:31 gram of magnesium carbonate at 10° C1. Pure
dolomite hence is far less soluble than either calcium or mag-
nesium carbonates, and thus its percentage in the rock should
slowly be increased, especially to the detriment of the carbonate
of lime, which in the first place formed the greater part of the
rock. The rock should then practically be a mixture of pure
calcium magnesium carbonate with pure carbonate of lime and a
small quantity of earthy ingredients. It should vary greatly in
the relative amounts of the carbonates of calcium and magnesium,
and the analyses, before mentioned, indicate that it does so;
Dana also from similar rock from the island of Metia noted 38:07
per cent. and 5:29 per cent. of carbonate of magnesium?
An additional factor in the formation of the dolomite might be
the large amount of magnesium salts raised in the sea-water of
the lagoons and pools in the reef at the time that these islands
were elevated. Dittmar in the Challenger Reports has shown
that magnesium chloride forms 10°878 per cent. of the salts in sea
water, and that other magnesium salts form nearly 5 per cent.,
while lime salts do not form quite 4 per cent. On the external
cliffs the spray from the sea might have some effect with a slow
elevation, but the specimens analysed from Namuka were both
taken from the inner side of the ridge; a series of analyses of
specimens taken at intervals from a short horizontal core obtained
from one of the outer cliffs would, however, at once settle the
extent to which this has been a factor of importance.
There is no method of estimating directly the amount of time
which would be required for this metamorphosis to a hard crystal-
line state. If it has taken place in the Lau Group as I suppose,
it should in course of time take place also in the raised reefs of
Viti Levu. It may be argued that traces:of such a metamorphosis
are not seen in other parts of the world, and that at any rate they
should be seen in the exposed limestone cliffs of Viti Levu. They
1 Handbuch der Anorganischen Chemie. Dammer tt. 2.
2 Loc. cit. p. 393.
4.70 Mr Gardiner, The Coral Reefs of [Mar. 7,
do show traces of a hardening on the surface, but the raised coral
reefs in Viti Levu, closely examined by me, are all overlain by
soapstone, a rock of such density and of such a nature that it
is very doubtful if it would allow water to percolate through it at
all. Considering the large size of the delta of the Rewa, it is
obvious that the eastern half of Viti Levu has been upheaved for
a considerable period of time, and hence it is only reasonable to
suppose that the upheavals which formed the Lau Group must
have been extremely ancient.
In Lau it has been seen that there are many perfect specimens
of raised atoll-reefs, of the same form as existing atolls, save only
that the slope is not gradual below their summits for some
distance and then precipitous, but at once an almost perpendicular
cliff. Naiau and Tuvutha are such raised atolls with perfect rims,
and lagoons apparently seldom more than 30 fathoms deep;
Mango has the rim broken and is deeper, probably from denuda-
tion. Kambara, once a typical atoll, has a broad flat rim, remains
of numerous shoals in a flat even lagoon, and many passages in
the original reef. Round Tuvutha are cliffs of over 100 fathoms,
and these are approached or exceeded by those of many of the other
islands. The cliffs are limestone; in no place except Lakemba,
where the raised reef is of the barrier type, is the foundation
visible. Considering the known sections of atoll-reefs, the pre-
cipitous cliffs to the sea can only be accounted for by the splitting
off of great masses of the rock, owing to undermining, and their
subsequent solution (or the formation on them of the fringing
reef). The reef sections of Funafuti! and of Sydney and Canton
atolls in the Phoenix Group? show that it is only at a distance of
150—200 yards from the edge of the reef that the steep com-
mences. Yet there is no trace of any distance approaching this
from the summits to the cliffs in such islands as Fulanga, Ongea,
Namuka and Kambara; indeed the edge of the cliff is often the
actual summit of the island. Hence the action of the sea under-
mining the cliffs must have been extremely extensive. As the
breadth of the fringing reef, supposing it to have been largely
built up on the fallen fragments, is in many places not comparable
to such an amount of undermining, it necessarily follows that the
solution under water of the fallen fragments must for some time
at any rate have kept pace with the breaking away of the land.
The higher elevations probably represent the highest points of
the reef, parts awash or low islands on the rim of the atoll; when
first upheaved, such would naturally be the most consolidated,
and hence least liable to solution.
Denudation owing to climatic causes cannot, I consider, have
1 Nature, vol. ty. 1897, p. 375. 2 Vide Admiralty Charts.
1898.] Funafuti, Rotuma and Fiji. 471
been of sufficient importance to have greatly affected the position
of the summits, or it should have left traces of itself in water
channels, ete. in the cliffs. It no doubt has been considerable, but
I think that the heights of the highest points are not far, not
more perhaps than 40—50 feet, below their original elevations,
when first upheaved. Crosby, in the case of El Yunque in Cuba,
has come to the conclusion that “erosion must have diminished
the height by as much as 200 feet?,’ but such an amount is
impossible for the Lau Group and seems to me very extreme for
that mountain.
That solution in the sea is taking place very rapidly admits of
little doubt from the presence of small lagoons within many of the
raised atolls. The beginning is seen in the pools in the centres
of Tuvutha, Naiau and other islands; in Mango these have further
dissolved themselves out a channel to the coast. Wangava is said
to have a tidal lake in the centre, while in Namuka and the two
Ongea, the water has broken through the reefs of the former atolls,
and opened lagoonlets to the sea; in their channels the water is
deep and within shoals gradually, denoting the extent to which
solution has taken place. Fulanga is an example of a later stage,
where a perfect lagoon, 10 fathoms deep, has been formed by this
means. The islands of its rim are high and protected from all
rapid solution oceanwards by the living reef, which now surrounds
them. The same action is, however, still going on within the
lagoon, the rocks of which, the shoals of the former atoll, are seen
to be disappearig one by one, and its ring of land to be lessening.
Only on the seaward face is any increase of the land visible, and
there is due merely to the growth of sand flats at the base of the
cliffs ; such flats, however, I only saw on this one limestone island
in the Lau Group. Should the Yangasa Group, as I am led to
believe from the appearance of their hills, be the remains. of a
raised atoll, they would form another stage, only a few isolated
peaks being left. Within the barrier Navatura and Yavutha are
connected by a reef awash, while the terraces on Yangasa Levu
I regard as caused by denudation in a channel through the
original reef; if they represent progressive steps in elevation, they
should rather have been separated by perpendicular cliffs. Finally,
some of the neighbouring atoll-reefs may possibly represent the
last stage, where all the raised reef has gone, and only the living
reef is left. In support of this I may here note that there are, in
addition, a number of large barrier reefs in the Lau Group, sur-
rounding very small islands, or rocks of a similar limestone to that
of these raised atolls.
The thickest cliffs, which I had the chance of closely examining,
1 On the Elevated Coral Reefs of Cuba. Proc. Boston Soc. of Nat. Hist. Vol. xxi.
1882-3.
472 Mr Gardiner, The Coral Reefs of [Mar. 7,
are all under 350 feet, but those seen on Tuvutha and Vatu
Vara are over 800, and those of Naiau, Mango, Vanua Vatu
and Vanua Mbalavu are about 600. The absence of terraces is
remarkable, as it is extremely characteristic of Tonga, the Solomon
Islands, and Cuba. One is driven from this to the conclusion that
elevation must have taken place for each island in one act to its
present level, or the undermining and wearing away must have
been still greater than I am prepared to admit: Thikombia-i-ra
is, I believe, an exception, as its terraces looked very distinct,
and it is in no way atoll-shaped; it stands also quite apart from
all the other islands.
Necessarily each island need not have been elevated to the
same height, but two areas of elevation are clearly defined to the
north and south of Lakemba, the elevation of which may have
been a separate act, as its limestone is nowhere thicker than
100 feet, and represents a barrier reef. Northwards the elevation
was about 700 feet, but southwards from Vanua Vatu to Ongea
about 400. The latter is very regular in neighbouring islands,
but yet great variety at the present day exists in the nature of
their living reefs. By Kambara and Wangava they are narrow
and fringing, while off Fulanga the reef is broader with a boat
channel. Namuka and Vanua Vatu have reefs both barrier and
fringing, while round the two Ongea the reef is typically barrier, but
slightly fringes the southern island. Round the Yangasa Group the
reef is a widely separated barrier with a lagoon 20 fathoms deep.
None of the pure limestone islands show their foundations, but
at Kambara the volcanic rock has welled out over the coral. This
island is otherwise typical of what a raised atoll might be supposed
to be, and here the nature of its foundation is exposed; it is also
shown in the same way in three places on Vanua Mbalavu. The
volcanic nature of the rock on Ono, Vatoa, Mothe, Lakemba,
Thithia, Kanathea, and Yathata proves that there must have
existed here a broad range of volcanic hills. The whole group of
Fiji stands on a plateau of 1500 fathoms, so that their general
height to bring them within the limits of coral growth, assuming
it at 50 fathoms, must have been over 8700 feet. Between the
islands and reefs of this range the depths are not usually marked
on the charts: in the Nanuka passage, and between Vatoa and
Ono there are a few soundings of considerably less than 1000
fathoms. There thus seems to be here a special ridge at 1000
fathoms, which possibly may be continuous southward with that
on which the Minerva reefs are situated. If so, it joims the line
of volcanic activity from New Zealand to the Kermadec Islands,
which then branches at the Minerva reefs through Tonga to
Samoa, and through the Lau Group of Fiji.
1 Vide Lister, loc. cit. p. 595.
1898.] Funafuti, Rotuma and Fiji. 473
I have already pointed out that several of the islands have
a greater thickness of limestone than 600 feet; Tuvutha further
is 800 feet high, and Vatu Vara 1030, with a cliff over 900 feet.
It is important to note that the latter is the greatest vertical
thickness of coral-limestone yet recorded. Prof. Crosby estimates
the thickness of the reef on El Yunque, Cuba, at 1000 feet but, as
he allows 200 feet for denudation, and the base of the mountain
consists of “eruptive rocks with some slates” and its summit is
“three-quarters of a mile long and a third as broad,” it is probable
that his estimate is far too high, much of the thickness perhaps
being due to the talus on the slope of the original reef.
I see nothing inconsistent, with any of the theories of the
formation of atolls and barrier reefs, in the shallow reef, together
with the talus slope, advancing outwards in a long period of rest
and so getting a spurious thickness. Darwin and Dana, however,
do not seem to have considered the possibility of such a period in
the slow subsidence they require. The real depth of the limestone
of Vatu Vara to the rock on which the island is founded might have
to be somewhat reduced owing to such a cause, but in contradistine-
tion to Kl Yunque the elevated reef of Vatu Vara is small at the
base and precipitous above, with a flat top not more than 100 yards
across in any direction. The same remarks may apply also to a
limited extend to Funafuti, where a thickness of 693 feet has
lately been obtained, and to Vavau, Tonga, where the cliffs are
500 feet high. Of other Pacific Islands Dana gives a thickness of
250 feet at Metia, Society Group, and of 300 at Mangaia, Hervey
Group; the sailing directions, however, for the Eastern Pacific
give the height of the latter island as 650 feet’.
In contradistinction to these Guppy asserts that the raised
reefs of the Solomon Islands are nowhere more than 150 feet
thick.
The mud, coating the bottom of the lagoon at Fulanga, has
apparently been formed by the wearing action of the sea on the
raised limestone cliffs. It has no trace, except in a few small
pieces of shell, of any organic origin, and is quite different from
what is known as coral mud. As Dana’s description? of the
chalk of Oahu, Sandwich Islands, applies equally well to this
mud, I would suggest that it was formed in a similar way, and on
upheaval solidified. Oahu has the same kind of hard limestone,
and the recurrent eruptions, which have taken place on that
island, might well account for all traces of its origin being lost.
1 Pacific Islands, Vol. 111. 1885, p, 14.
2 (oc. cit. p. 395.
474 Mr Gardiner, The Coral Reefs of [ Mar. 7,
RAR ave
SPECIAL FEATURES IN THE NATURAL HISTORY OF CORALS.
Section 1. The Structure of a Reef.
I have already described fully the external appearances of the
coral reefs of Funafuti and Rotuma. In Fiji the reefs, which are
freely exposed to the ocean, have all a well-defined rim and reef-
flat; some also have a boulder zone, which is naturally absent
from the reef at Funafuti owing to the elevation of that atoll.
Few have such a luxuriant growth of corals as are found on the
reef-flat off the windward end of Rotuma, but otherwise their
differences are merely differences in detail.
The boulder zone shows, I think, the distance from the edge of
a reef, at which boulders can be piled up on the reef-flat to form,
subsequently, land. From the Penguin the outer reefs on the
windward side of Nukulailai, an atoll about 65 miles south of
Funafuti, could be seen to be as narrow as in the similar position
at that atoll; on the other hand the same reefs off the leeward
island are as broad as on the leeward side of Funafuti, but with no
rough zone. In this position at Nukulailai there is a rim much
broken up by fissures, followed by a reef-flat upwards of 200 yards
broad, hollowed out for 2—3 feet with, im places, pools of water
5—6 feet deep; this extends to the island itself, which is not more
than 2—3 feet above the high-water level. The island is formed
principally of small boulders and sand, and rests on the reef-flat
all round, so that the latter has a total breadth of over 600 yards.
This atoll differs greatly from Funafuti, as its lagoon is almost
completely encircled by the reef and has everywhere a sandy
bottom. Land too encloses the greater part, the broadest gaps im
it being to the north-west and south-west. There are a few
isolated blocks of rock on the reef, but these are not regular in
position and seem rather to be negroheads than pinnacles; they
are more abundant to leeward.
From the appearance of the atoll of Nukulailai I should not
judge that any upheaval is necessary to explain its characters ;
there may, however, have been one of 2—38 feet. The reef to the
south-west, where there is no land, bears a close resemblance to
that on the west side of Wakaya, Fiji. It consists of pools of
water 1—10 feet deep, fringed with corals, nodulose, and laminated
nullipores; Millepora is everywhere very common, as also is
Heliopora, a genus only found at 35 fathoms off Funafuti. The
1898. ] Funafuti, Rotuma and Fiji. AT5
islands to windward seem to have been formed by an aggregation
of boulders, and their subsequent consolidation underneath by the
deposition of carbonate of lime, caused by the evaporation of the
spray and salt water at low tide. The large island to leeward
appears to be a large sand cay on the reef, formed partially by
fragments of reef-rock, but principally by sand washed up from
the lagoon and formed into a bank by the assistance of the wind.
The lagoon has a depth of about 10 fathoms, and is stated by the
natives to be of a basin-like form, rather than a flat with pre-
cipitous walls. As the tide falls, the water rushes out of the
lagoon by a few narrow passages, which, however, would seem to
be insufficient to keep its water at the same level as that of the
external ocean; hence it is probable that (as the natives stated)
there are tunnels from the lagoon, which assist in carrying away
the water. It is interesting to note that on the western island of
Nukulailai there is a spring of pure fresh water, which, according
to the natives, is continually running. This probably indicates
that the foundation of this atoll is situated at no great depth. I
was informed by Capt. Wilson that Arecifos, or Providence Island,
to the east of the Marshall Group, has also a spring of clear fresh
water in the coral-rock, and that this and Nukulailai are the only
coral islands in the Central Pacific, where such are found.
The appearance outside a reef is that of a number of more or
less overhanging and anastomosing masses of rock with pools
between, having sandy bottoms. The same appearance is retained
on protected reefs, until they become awash, when by the growth
of corals and nullipores the masses fuse, and a smooth platform is
formed. ‘The inner part of the Great Barrier Reef of Fiji consists,
where it is single, of deep pools, separated from one another at the
surface but joined below. Inside the more solid outer part of the
reef here mushroom-shaped heads of coral rock grow up, anasto-
mosing with one another at the surface to form an almost solid
platform, resting on so many large pillars. I have obtained, in
pools on the inner parts of the Great Barrier Reef and of the reef
to the west of Wakaya, 5—6 fathoms of water, and at the same
time noticed that the tide sets strongly through them, indicating
a free connection with the ocean beneath the surface. Outside
reefs, where they are exposed to the ocean, there seems to be the
same process as within the Great Barrier Reef, but the joming
organisms are almost entirely nullipores; in the account of the
outer reef of Funafuti I have shown how it is going on at the
surface, and it certainly seems to be taking place outside the
rim. At greater depths the same formation also, I believe,
occurs; the corals and nullipores cannot grow upwards with
such vigour as inside the reef on account of the strong back-
wash of the waves which break on the reef, and so grow relatively
476 Mr Gardiner, The Coral Reefs of [Mar. 7,
more outwards, and anastomose more frequently with one another.
The whole structure then, provided that there are no movements
of elevation or subsidence, should be an open spongework, full
of chambers and passages, some of which are partially, or com-
pletely, blocked by sand and boulders.
The consolidation of sand and fragments by the infiltration
of sea water is not, I believe, of any importance. That molecules
of a salt can out of a saturated solution of that salt attract
more molecules admits of no doubt, but there is no evidence to
show that this is going on with regard to lime salts to any con-
siderable extent in the sea; the pores of the dead corals in
reef-flats and in the raised reefs of Viti Levu do not show any
marked filling up, which can be ascribed to such a cause. Sand
is constantly to be found in small holes in the reef completely
walled in by the growths of nullipores and corals; it exists also
in greater or less quantity in nearly all the pools on the reef,
in all boat channels and on all inner reefs, but I could not
succeed in finding it consolidated together in any way or to the
rock below it under low tide level. The sand in the soft limestone
quarry at Suva, although it has evidently been upheaved for a
considerable time, is still badly consolidated, and the thin layer
between this rock and the soapstone is almost loose. The Report
on the Coral Reef at Funafuti by Prof. Sollas mentions that loose
sand and boulders were met with as deep as the bore went. At a
depth of 72 feet in the bore, on the outer sides to windward of the
atoll “the bottom of the hole was surrounded by quicksand, con-
taining boulders of coral, and as fast as the sand was got out, so
fast it flowed im and faster.” The consolidation of the fragments
here has certainly not been effected, and I am inclined to doubt
whether infiltration does not have an entirely opposite effect by
means of the carbonic acid gas in the water.
The hard parts of a reef, above low tide, are made up of frag-
ments of coral, sand and nullipores, the consolidation of which
seems to be due to the deposition of carbonate of lime on the
evaporation of the water at low tide. Loose fragments after a
time get a bed of fine mud, which, as more fragments are piled up,
gradually surrounds and buries them. On the reef-flat there is
less coral and less sand, and much of the rock is formed by a
structureless and very compact limestone, which also forms the
whole rim. Where corals are found in this rock, they are not as a
rule as much eaten into or worn, as they are in the parts above
the low tide level; they do not seem like fragments at all, but as
skeletons of corals in the position of growth. This appearance leads
me to believe that the rock here has grown up to the surface exactly
in the position in which it is found, and is not made up of masses,
thrown up from outside the reef by the seas and cemented together.
1898. ] Funafuti, Rotuma and Fiji. ATT
Of the structure of the surface of a reef Dana gives the follow-
ing account :—“The reef rock, when broken, shows commonly its
detritus origin. Parts are of compact, homogeneous texture, a
solid white limestone without a piece of coral distinguishable and
scarcely an imbedded shell. But generally the rock is a breccia,
or conglomerate, made up of corals cemented into a compact
mass, and the fragments of which it consists are sometimes many
cubic feet in size.”
The last sentence certainly will not apply to the reefs of Fiji.
The parts of “compact homogeneous texture” are very numerous,
and are formed, I believe, mainly of the carbonate of lime secreted
by incrusting nullipores. The importance of the incrusting nulli-
pores, in the formation of the reefs of the Central Pacific, cannot
be overestimated. The greater part of the rim of the reef and its
outer slopes is covered by these algze. A coral dying is at once
grown over by them; sand grains and even loose boulders are
enclosed, and fissures as well as small pits are bridged. These
incrusting nullipores grow close to the surface they are on, and
spread gradually outwards, fixing themselves as they grow, so that
they form a very strong bulwark against the sea. At the bottom
of the sea, outside the reef in 7—15 fathoms, they often form on
the tops of the ridges large nodular masses round fragments of
coral and rock; the smaller nodules (which alone could be loosened
by the use of Priestman’s grab) showed thicknesses of upwards of
4 inches of compact white homogeneous limestone secreted by
them, and I have no doubt that by their agency the greater part
of these large masses was formed.
The incrusting nullipores of the reef belong to the genus
Lithothamnion, which Walther has shown covers and has ap-
parently formed the greater part of certain shoals in the Bay of
Naples’.
Walther afterwards investigated the tertiary ‘“ Nulliporen-
kalk” of Syracuse, and found all stages from well-preserved
specimens of Lithothamnion to a structureless limestone. Of the
lias of “'Todten Gebirges ” it is remarked that “the strata consist
of coral rock, detrital calcareous deposits, and associated with
these, masses of limestone, in which microscopic examination fails
to detect either vegetable or animal structure. These structure-
less beds are considered to have been Jithothamnion banks from
which percolating water has removed all traces of algal cells*.”
The outer reefs of Fiji, Rotuma, and Funafuti seem as if they
1 Loc. cit. p. 175.
2 Die Gesteinbildenden Kalkalgen des Golfes von Nene’ ete. Zeitsch. deutsch.
Geol. Ges. xxxvu1. 1885, p. 329.
3 Algea as Rock- building Organisms. A. C. Seward. Sci. Progress, Vol. 1.
1894, p. 19.
VOR (x, PT. Vil. 38
478 Mr Gardiner, The Coral Reefs of [Mar. 7,
form structures, which, if upheaved, would give a rock precisely
similar to this.
In the lagoons, it must be remarked, the shoals are formed
much more of corals and have everywhere precipitous sides. Nodu-
lose, mamillated and laminated species of Lithothamnion grow,
but, while they are often very abundant, they cannot have the
same binding effect as the incrusting forms. Algze of the genus
Halimeda, Mollusca and Sarcophytum abound, and the whole rock
seems a somewhat loose conglomerate of the remains of all these,
held together mainly by coral growth.
SECTION II.
THE BATHYMETRICAL Limits oF CoRAL GROWTH.
Dana on this subject sums up the evidence to 1890 in these
words * :—“ There is hence little room to doubt that 25 fathoms or
150 feet, may be received as the limit in depth of flourishing
banks of reef corals.” Although I cannot admit some of the
arguments that he urges in favour of this view, there is really no
evidence which proves that “flourishing banks of reef corals”
grow at a greater depth; indeed it would be equally correct, if
Dana placed the depth at 15 fathoms, which is about the limit of
the visible zone.
Yet I think that, considermg the few dredgings that have
been taken outside coral reefs and in spite of the few species
of incrusting and massive corals, which have been brought up,
there 1s now strong presumptive evidence that corals live down
to depths of 40—50 fathoms in great luxuriance. Dr Bassett
Smith’s dredgings on the Macclesfield Bank showed that 18 genera
of corals with 40 species were living at depths from 20—44
fathoms”. “The following 10 genera were found at a greater
depth than 30 fathoms :—Stylophora, Astraea, Pavonia, Cycloseris,
Leptoseris, Stephanaria, Psammocora, Montipora, Alveopora and
Rhodaroea, besides seven small scarcely reef-building genera.”
The total number of species collected was 142, so that nearly one-
third were represented in depths over 20 fathoms.
The character of the reef off Rotuma is certainly such as to
indicate a growing coral bed to depths up to 40 fathoms, and the
soundings and dredgings off Funafuti give for this atoll a similar
depth. The dredge and the swabs when placed down in depths
of 20—40 fathoms were constantly caught up, and their whole
behaviour indicated such a very rough and uneven bottom, that
1 Loe. cit. p. 118. 2 Nature, Vol. xu. p. 223.
1898. ] Funafuti, Rotwma and Fiji. 479
I had no doubt that it must have consisted of a growing coral
bed, of which Dana remarks *:—“ The character of a growing coral
bed is so strongly marked in its uneven surface, its deep holes
and many entangling stems, to the vexation of the surveyor, that
in general the danger of mistake is small.”
At Funafuti, eight dredgings were made on the steep slope of
the reef between 40 and 140 fathoms, none of which gave any
evidence of reef-building corals at these depths. There were a few
patches of solitary corals, but even these were rare on the stones
brought up. At a depth of 35—45 fathoms off the south end
I took a haul of the swab and obtained four species of Madrepora,
three of which I have identified with M. reticularis, M. angulata,
well-known deep living species, and MM. scabrosa. No other true
corals were obtained, but there were two small pieces of Helvopora.
At a greater depth than 30 fathoms, also off the south end, I
obtained in two hauls three species each of Pocillopora and
Madrepora, and one each of Stylophora and Porites; there were
also several small pieces of Millepora. Off the north of the island,
I could not keep in these depths as the slope of the reef was
too abrupt, but one long haul, with the shallowest depth 21
fathoms, resulted in three species of Madrepora, one each of
Heliastrea and Pocillopora, and also several pieces of Millepora.
In all, from depths of over 20 fathoms were obtained 7 species of
Madrepora, 4 of Pocillopora, and one each of Heliastre, Porites
and Stylophora, making in all 13 species in four hauls of the
swabs. Outside the reef, five hauls of the swabs at depths up to
7 fathoms gave in all 11 species, represented by 5 Madrepora,
2 Pocillopora and one each of Seriatopora, Montipora, Porites
(apparently P. arenosa, a very common species on the shoals of the
lagoon) and Stylophora. Millepora was, however, very common in
all the hauls up to 7 fathoms, and evidently grows extremely
luxuriantly at about this depth.
SECTION III.
THE Foop oF CoRALS.
The conclusion of Murray’, “that the chief food of the corals
consists of the abundant pelagic life of the tropical regions” does
not seem to rest upon many direct observations, though the same
statement is repeated, or inferred, by nearly all writers on the
theory of the formation of these reefs. A further conclusion is
Teloe2 Clnpa lilt.
2 Coral Reefs. By Chas. Darwin, 1889. App. 1. p. 286.
38—2
430 Mr Gardiner, The Coral Reefs of [Mar. 7,
then drawn by Murray that “when coral plantations build up
from submarine banks, they assume an atoll form owing to the
more abundant supply of food to the outer margins and the
removal of dead coral rock from the interior portions by currents
and the action of the carbonic acid dissolved in the water.” With
the latter statement we are not at present concerned, but that the
more abundant supply of food to the outer margins causes these to
grow up quicker, Iam inclined to doubt. I have already stated that
I do not consider that the Madreporaria, together with Heliopora
and Millepora, are the chief factors in the formation of coral reefs
within shallow depths, as Murray seems to infer, but at the same
time I do not deny to them a very considerable influence.
At Funafuti I did not have many opportunities of examining
the “auftrieb” outside the reef, and none in the early morning,
when it is always most abundant near the surface. On the few
occasions that I used my nets outside the atoll I found that the
deeper I sank them into the water, up to 50 fathoms, the greater
were the quantity and variety of pelagic animals obtained. Near
the surface and down to 25 fathoms the nets were useless, and on
no occasion did I find, even at 50 fathoms, a luxuriant pelagic
fauna. This proves nothing, but it indicates that, at any rate
during the daytime, the fauna must sink down to very considerable
depths; unfortunately I had neither the time nor the opportunity
to investigate depths below 50 fathoms. In the lagoon, the
surface fauna, before daybreak, is generally very rich in the
pelagic larvee of Crustacea (especially the Phyllosoma), pelagic
Crustacea and Sagittu. There are usually found in addition
veliger and trochosphere larve of the Mollusca, and larvee of
Tunicata, Chsetopoda, fishes and Echinodermata. Pteropoda,
especially of the genus Creseis, are occasionally very abundant,
while the remainder of the “ auftrieb” is almost entirely made up
of bits of green seaweed, dirt, etc. Before dawn, nets at 10, 15,
and 20 fathoms in the lagoon give only a few Sagitta, but a large
amount of sand, with bits of weed, etc. in suspension. After
dawn, the fauna for an hour can be followed down, as it sinks
from the surface, and is obtained progressively in the deeper
nets. At midday, even the deepest nets in the lagoon almost
failed to obtain any animals; the whole fauna seemed to sink
until it les in the layer of water which immediately covers the
bottom, as it was found, when a net was accidentally scraped
along the bottom, that with the dirt brought up there was a
decidedly rich fauna. Generally outside the atoll the fauna was
the same, but unicellular algee and Radiolaria are at times very
common. At Rotuma I fixed my “auftrieb” nets in the passages
of the reef to find out what animals were driven over the reef to
form the food of the corals on the reef-flat and in the boat
1898.] Funafuti, Rotuma and Fiji. 481
channel. This fauna differed little from that inside the lagoon
at Funafuti; but Radiolaria were more abundant, and often the
pelagic eggs of different species of fishes were extremely numerous.
Bits of green weed and pelagic alge were very common, but
there was little sand, or dirt of any sort. When the tide was
ebbing the nets gave few animals; there was generally, however,
a large accumulation of sand with bits of weed in the bottle.
In the “auftrieb” collected in the daytime at Rotuma, animals
were rarely to be found, while the fauna at night was very rich.
In agreement with this it was noticeable that only at night time
were the corals of the family Astreeide fully expanded; these
corals expand somewhat on the tide rising, but I never saw any
with the exception of Huphyllia, Symphyliia and Mussa fully
out in the daytime, while at night parts of the reef looked quite
different by reason of the expanded polyps.
The examination of the food, found in the celenteron of
different species of Prionastrewa, Favia and other genera, killed
in the early morning, was unsatisfactory. In most I could only
find pieces of green weed with sometimes a few small, oval, uni-
cellular algze; animal remains were rare, and could seldom be
identified. I next tried to feed different species of corals, placing
them in bottles, into which a certain amount of the “auftrieb”
from the passages in the reef was poured, and then sinking them
in a pool off Solkopi; I could get no results with any genera,
except Huphyllia and Mussa. Other genera with large calices,
such as Prionastrwa and Favia, could not be obtained in small
enough pieces without damaging some of their polyps, and, after
removal from the mass, were rarely found expanded either by
night or day; these two genera further were never seen ex-
tended in the daytime, while most of the pelagic animals in the
bottles, although they were sunk in 4 feet of water under an over-
hanging ledge of rock, never lived more than a few hours. The
different polyps of the species Huphyllia and Mussa, on which I
experimented, were not in physiological continuity ; increasing by
fissiparity, their calcinal centres soon become very distinct, the
corallites separating, and never remaining in long series. As the
living tissues only cover the top $—# of an inch of the corallum,
the branches, where they are broken off, are dead and these corals,
when placed in the bottles, easily expanded. The animals in the
“auftrieb” gradually became less active, until they moved but
slowly over the bottom, so that the conditions should have been
eminently favourable for the polyps. The tide would not allow
the polyps to be kept in the position I chose for more than four
hours, so that in about this time the bottles were lifted and the
corals killed by being dropped into a saturated solution of corrosive
sublimate.
482 Mr Gardiner, The Coral Reefs of [ Mar. 7,
I examined eight calices, thus fed, on five branches of Huphyllia
gaimardi; they all showed an abundance of unicellular alge and
were mostly stuffed with pieces of green seaweed. The eggs and
larvee of Mollusca and Echinodermata were common in all, and in
some also fish eggs; there were a fair number of Radiolaria (9)
identified and also the remains of some cheetopod larvee. In
addition, one Nauplius larva, one Appendicularia larva, two Sagitta
and two Atlanta were observed. In seven calices of the Mussa,
experimented on, unicellular alge and pieces of seaweed were
very common. There were also identified two Ceratia, one
Radiolaria, one crustacean (apparently Vebalia or a larva allied to
it), some Protozoa like Noctilwca and the remains of a few Meduse.
All the “auftrieb” in Rotuma was very rich in crustacean larve,
and Sagitéa, but these, although they had nearly all sunk, when
the bottles were lifted, did not seem to have been consumed by
the polyps.
In accordance with a suggestion of Prof. Hickson, I took
especial note of the colours of the different species of corals. On
our arrival at Funafuti the whole party was struck with the
colours of the Pocillopora living on the outer reef; some were
a brilliant pink, others an equally brilliant green, and others
almost colourless. Closer examination showed that the latter had
their calices coloured light green also, and I found that the green
coloured forms had the polyps expanded and the colourless con-
tracted, and so I concluded that, when contracted, the green forms
would be almost colourless. There was one species, living in the
fissures of the reef, which showed all three appearances, pink,
green, and colourless; I brought back more than a dozen pieces of
it, to see if they were different species, but all can be identified
with Pocillopora grandis (Dana). I fixed two bottles firmly on
the top of two branches of one of the green forms with tow round
their necks and two also on branches of one of the colourless
forms. Three days afterwards I found at the top of each bottle
on the green forms a few cubic centimetres of gas, and about one
centimetre at the top of the other two bottles. The gases from
the first two bottles added together seemed to make the spark at
the end of a match glow and so to indicate the presence of oxygen;
the result from others was unsatisfactory. I soon after had to
leave Funafuti and unfortunately at Rotuma this species was only
once obtained. Other Pocillopora, most of which are green, gave
for a long time unsatisfactory results, as it was hard to remove
this coral from the reef without damaging it, and the species were
too small and too exposed to fix bottles over them. Finally I
placed in bottles six pieces belonging to one or more of the
following species of Pocillopora, between which at that time I did
not properly distinguish :—P. verrucosa, P. lacera, P. lobifera,
1898. ] Funafuti, Rotuma and Fi. 483
and P. brevicornis. These bottles I fixed upside down with open
mouths in a pool off Solkopi, where there was a free circulation of
water, but no sand or dirt; at low tide they were covered by
4 feet of water and their position was one in which they would be
fully exposed to the light. At the end of a week five bottles
were happily unbroken, and of these, four had a small amount
of gas in each. The gas was then all collected together into a
tube, which was next held in the water over a small piece of
metallic sodium in a perforated tin box, until twice the quantity
of hydrogen gas was added to the other gas. The tube was then
removed and, on being turned up, a lighted match was placed at
its end and, the thumb being removed, a distinct explosion re-
sulted. From the four pieces of Pocillopora, only about 8 cms.
of gas were obtained in a week; the same experiment, however,
carried out for a like time with four pieces of Prionastrwa (the
species being taken from the rim of the reef, but not distinguished
specifically) gave upwards of 15 cubic centimetres of gas, which
exploded in a like manner. From Huphyllia gaimardi, over the
polyps of which I fixed the bottles without breaking their stems,
I obtained an even greater amount of gas, into which I placed a
glowing match, which at once burst into a flame. Madrepora, if
broken, gave very little gas, but over some of the branches of a
species which grows very abundantly on the reef-flat, and in the
pools off Solkopi, I fixed bottles; the gas given off, though not as
great as from the Pocillopora, also gave an explosion, 1 further-
more proved that gas was given off from a species of Fungia,
and I had traces from several Favia and one Stylophora; my
experiments, however, on these genera were unfortunately
shortened by a strong gale in the end of November, 1896, which
broke all my bottles.
Pavonia divaricata and Pavonia cristata, which were also
very abundant in the pool by Solkopi and over which I fixed
bottles, gave negative results, as also did some experiments on
Porites and Astrwopora in the boat channel. Heliopora and
Millepora abounded in the boat channel, but no gas from them
was obtained, although they were especially carefully managed.
On the whole the experiments were not altogether satis-
factory, as the amount of gas, given off by different pieces of
the same species, varied much more than the sizes of the pieces
did. All the reef species of Prionastrwa and Pocillopora were, I
believe, experimented on and never failed to give a certain
amount of the gas, but the different species of Havia were un-
certain. It would have been interesting to discover how much
of the gas given off was oxygen, by exploding it by means of a
battery, but experiments to this end were unsatisfactory owing
to the want of proper apparatus.
484 Mr Gardiner, The Coral Reefs of [Mar. 7,
The spirit material I brought from Rotuma is unsatisfactory, so
far as I have examined it. Some sections, however, of Huphyllia
and Prionastrea polyps show apparently the presence of uni-
cellular algae in the endoderm and structureless lamella.
Prionastrea and Pocillopora, the two genera which gave by
far the best results, both live on the rim of the reef and are
uncovered, though never dry, at low tide. Should the giving off
of oxygen, as my experiments seem to indicate, be confined to
certain genera it would be of interest to note their distribution on
the reef, and in depth. That oxygen is given off, I do not believe,
to be due in all cases to parasitic alge; in the genus Madrepora
I have completely failed, so far, to find any such, and while the
species of this genus only gave off small quantities of gas, all the
species yet gave off a certain amount. Experiments at Wakaya,
Fiji, on species of Pocillopora and Prionastrea, fully confirmed
my results in Rotuma, though the quantity of gas seemed relatively
less. I do not know how far the gas in some cases may not have
been due to the alge in the ccelenteron, but I do not think
this factor is of any importance. As the species of Madrepora
and Pocillopora, obtained from depths off Funafuti up to 35
fathoms, all had their corallites distinct to the eye, like pins’ heads,
when fresh, and of a dark greenish colour, it seems to me probable
this assimilation of carbon from carbonic acid gas is a very 1m-
portant factor in the growth of corals and hence in the formation
of coral reefs.
SECTION IV.
CONDITIONS AFFECTING THE GROWTH OF CoraL REEFS.
Most of what I have now to draw attention to under this
heading has been already anticipated in my descriptions of the
different reefs. I have, in connection with many of the reefs,
referred to the effects of currents, of which two kinds must be
distinguished, namely, tidal and ocean; the first are usually
shallow currents, but the latter are both surface and deep, and
do not, I think, vary much in the central and western parts of the
Pacific with moderate winds. The tidal currents show their
influence mainly in the passages of reefs and inside reefs, while
the ocean currents affect rather the growth of the whole reef. In
fringing reefs the passages are generally free from corals, which
nevertheless sometimes grow very luxuriantly, where the tidal
current commences to spread out over the whole boat channel. It
is In this position, where the current slackens, that sediment would
1898. ] Funafuti, Rotuma and Fi. 485
be deposited, rather than in the passages themselves in which the
absence of corals is more probably to be accounted for by the
inability of the larvee to fix themselves. The ship’s entrances at
Fulanga and Lakemba in the Lau Group of Fiji, where tidal
currents of 4—5 knots an hour are met with, are very free from
corals, which yet live in great luxuriance off their entrances as
deep down as the bottom can be seen. At Funafuti, in the ship’s
entrances, the genus Millepora is extremely abundant, but true
corals are rare.
With regard to ocean currents, which, in some groups of islands,
are very powerful in certain positions, I think that they probably
modify considerably the form of the whole reef, by preventing the
proper fixation of the larvee both of corals and nullipores, and by
the distribution of the talus on the reef slopes. The form of the
channel, between Wakaya and Ovalau, is probably due to this, the
slope being very sharp down to 40 fathoms off each island, where the
steep is reached, the reefs on either side running also very evenly,
and with few projecting points. Such currents as cannot pass this
way must pass to the south of Viti Levu, and all along the coast
here the reef lies close to the land. The current between Taviuni
and Vanua Levu is not altogether tidal, but probably has had a
still greater effect on the reefs. I cannot entirely agree with
Semper!, when he states his opinion that currents are one of the
principal causes which have given the reefs their very remarkable
forms. Given a bank at a suitable depth, I think that it would
require a very powerful current, a current such as is only found in
narrow straits between islands, to prevent a reef from forming on
it in suitable latitudes.
Where currents are not too strong, they assist no doubt very
materially in the formation of the reefs in some way. Most atolls
have their land to windward and thei passages to leeward ;
Charybdis reef to the north of Viti Levu, a case in point, is well
protected against the wind, but its reef is, apparently owing to the
current, especially well formed to the east but quite open to the
west. In the Gilbert Group the current and wind both come from
the east, on which side also the land generally lies. In the Marshall
Group, the current sets east and the prevailing wind is east-north-
east, the two being thus opposed to one another; the atolls have
therefore land both on their windward and leeward sides.
At Rotuma corals are found in greatest abundance in the boat
channel at points intermediate to passages in the reef. Before I
observed this, however, I removed specimens of a number of
different species down the coast for about half a mile to a position
almost opposite to a big passage—from an area very rich in corals
1 Animal Life. By Carl Semper, 1881, p. 229.
456 Mr Gardiner, The Coral Reefs of [Mar. 7,
to one proportionately poor—so as to observe them constantly and
have them handy to kill, when they were properly expanded. I
fixed them between stones on the sandy bottom, but they soon
became silted up with sand and were killed. I then placed a
number of pieces on the hollowed out top of a species of Astrwo-
pora, but debris soon collected round them, and, when I last visited
them, I found only the clean coralla without polyps. Generally I
could not, in the boat channel, get any true coral to grow if placed
on the bottom owing to the sand and mud deposited on them, but
all would grow if not too near the passages, on the tops of the
stone heaps, which are built up by the natives for fish trapping.
In the few fringing reefs, with boat channels, which I examined, in
Fiji it was unusual to find any corals growing inside the reef, and
at Rotuma the presence of corals is largely due no doubt to the
presence of these stone heaps, on which the larvae fix themselves
above the level of the scour of the tide. j
When I saw that the corals on the Astrwopora were being
killed, I tried transferring all the commoner species out of their
own peculiar zones into other zones. I also wounded a certain
number of corals over a definite area to see how soon their wounds
would heal and be grown over. Of course in the limited space of
three months no decisive experiments could be carried out, the
results are yet not without interest. Broken-off arms of branching
species and small pieces of massive species all died. . Branching
forms removed by the root and large blocks of massive species, if
kept in their own proper zone, continued to live. Corals could be
removed from the rim to the reef-flat ; from the nature of the reef
_ it was impossible, however, to try the opposite experiment. Some
species from the reef of Pocillopora and Prionastrwa, fixed on the
top of a stone heap near one of the passages, seemed to flourish,
but species of Madrepora and most other genera died. In no case
was there any sign of the coral attempting to fix itself. The polyps
near the damaged part of a colony died, and there was no attempt
in the time to heal over the scars, which simply gave an easy
entrance to boring animals. The experiments with Millepora and
Helopora were inconclusive; their lamellae fixed on the hollowed
out top of the Astrwopora certainly seemed alive after three
months.
I never saw the corals over any considerable area, or individual
corals, killed by the heat of the sun at low tide. The corals on the
rim, at even the lowest tides, are constantly wetted by spray, and
on the reef-flat the water remains constant in height. In the boat
channel at Rotuma, and on certain shoals at Funafuti, I noticed
species of Montipora, Porites, Favia and many other genera exposed
for upwards of three hours at low water without any effect on them.
Nearly, if not all, had some part in the water, and doubtlessly
1898. ] Funafuti, Rotuma and Fiji. 487
water can be passed on by diffusion, or in some other way, from
polyp to polyp. At spring tides at Rotuma, parts of the Heliopora
and Millepora clumps in the boat channel were exposed for four
hours. I examined them when they were thus exposed, and also
on my return from the reef after the tide had turned, when they
were just covered, and found that all the polyps of the Heliopora
were expanded fully and those of the Mullepora partially so. I
found, too, that true corals also tended to partially expand on
being immersed again.
The effect of rivers is due more to the sediment which they
carry down in suspension, than to the freshness. of their water.
Yet at the chief mouth of the River Rewa, the bottom is hard
from the edge of the reef for some distance up the river, and
corals are absent from the whole of the inner part of this area.
The streams on the east of Taviuni vary enormously in size and
very quickly run down; the reef outside, where it exists, is well
formed and covered entirely above the low water level by Litho-
thamnion. The fresh water, being lighter, must spread out in a
sheet, when it meets the ocean, and yet the reefs, in the neigh-
bourhood of the Rewa, Navua, Penang and Lambasa Rivers, are
all well developed and awash at low tide.
SECTION. V.
THE RATE OF GROWTH OF CORALS.
I had an opportunity of assisting in cleaning the chain of a
buoy, which had been down in Levuka Harbour, Fiji, for one year
and ten months. The first, or upper, fathom of chain had no
corals, but was covered completely with Tunicata, bivalve Mollusca
and sponges. In the next two fathoms I obtained six different
coral growths which with their weights were as follows :—
1. Turbinaria 45 grams.
2. Pocillopora 41 and 13 grams.
1. Helastraea 34 grams.
1. Madrepora 20 grams.
1. Galaxea Two corallites weighing nearly 1 gram.
A rusty iron chain is not likely to be a good foundation for
the corals to fix themselves on, so that these growths in this space
of time are most remarkable.
438 Mr Gardiner, The Coral Reefs of [Mar. 7,
PART Wa:
THE FORMATION OF CORAL REEFS.
The generally accepted theory of the formation of atolls,
before Darwin brought forward his well-known theory of subsi-
dence, was that they were situated on the rims of submarine
voleanoes. It is possible to explain the formation of atolls quite
satisfactorily on this theory, if such craters really can and do exist
at the requisite depths. Prof. Sollas, without expressing an
opinion, has drawn attention to the striking similarity of the
slopes of Funafuti to those of a volcano’. “The conical mountain
below the 140 fathoms line, with its parabolic slope is suggestively
similar to a volcano; but if so its crater must have been immense,
10 miles across at least.” Many arguments can be advanced
against the possibility of there being such large craters and such
a large number, as would be requisite to account for the founda-
tions of the atolls of the Indian and Pacific Oceans. No volcanoes
with craters even as large as the medium sized atolls and atoll-
reefs exist at the present day; and there are no indications,
except in the Andes, of such large chains of volcanoes as would be
requisite to form the Ellice, Gilbert and Marshall Groups, which
form a line as if of one mountain chain. Another great objection
to this theory les in the fact that it leaves the formation of
barrier reefs completely out of account, and anyone, who has
examined both atoll and barrier reefs, cannot fail to have been
struck by their striking similarity to one another. Again, there is
found every intermediate variety from the narrow fringing reef to
the atoll with perhaps the greater part of its rim converted into
land.
It is, however, very doubtful whether a submarine crater could
be formed as such; lava meeting the water would usually break
up into loose vesicular cinders and ash. Falcon Island, Tonga, is
said? to be “just a bare brown heap of ashes.” Sir A. Geikie
mentions* Graham’s Island, Sicily, erupted 1831, Sabrina Island,
Azores, 1811, a new island in the basin of Santorin, 1866, and an
island formed in 1783, 30 miles west of Cape Reykjanaes, Iceland,
all of ash, and either completely worn away or being rapidly
destroyed. The only permanent cone, known to have been thrown
up by a submarine eruption, is the island of Johanna Bogoslawa,
1 Loc. cit., p. 375.
2 «The Newly Emerged Falcon Island.” By J. J. Lister. Proc. R. G. Soc.,
March, 1890.
3 Text-Book of Geology, 1893.
1898.] Funafuti, Rotuma and Fit. 489
Alaska, 1796; it is 3,000 feet high. Captain Dawson, H.MLS.
Waterwitch, informed me that in the eruption of Ambryn, New
Hebrides, in 1895, the lava where it met the water in its flow,
burst into fine cinders and ash; of course under the ash the lava
might possibly still flow. Further, so far as I am aware, no deep
banks of crater-form have yet been discovered in the sea. The
foregoing is sufficient evidence to make it very doubtful whether
craters can be formed under the sea, and if the foundation of any
atoll should be on the top of a crater; I consider it can only have
been thus formed owing to the subsidence of the crater. The
island of Totoya, about 1° due west of Kambara, Fiji, is the
remains of an extinct crater, 3 miles across and 1184 feet high,
with the south side blown out; it now has a depth of 30 fathoms
of water in the original crater. If it subsided 1300 feet, an almost
perfect ring of coral would grow up, but it would take a very long
time for the crater to fill up to 30 fathoms, the usual depth of an
atoll; and whether it could ever do so, on account of its opening
to the south and the consequent scour inside, is doubtful. I can
find no atoll or horse-shoe reefs with depths in any way approach-
ing this, and I conclude that it is absolutely necessary to reject
this theory in its entirety, as applied to any atolls.
Darwin’s theory has, however, a great advantage over all others
which have before or since its publication been put forward, in
that it explains all the different forms of reefs on the same hypo-
thesis. There can be from the nature of the case little direct
evidence brought forward of subsidence. “There is,” Dana writes?,
“not merely probable but positive evidence of subsidence in the
deep coast indentations of the high islands within the great
barriers. The long points and deep fiord-like bays are such as
exist only where a land, having been deeply gouged by erosion,
has become half submerged.” Such evidence as applied to
volcanic islands is, I submit, of very doubtful value. Viti Levu and
Vanua Levu, according to Dana’s views, must have subsided
at least 1000 feet, and, as there are practically no atoll or barrier
reefs with land on their rims in the Fiji Group, it must be still
subsiding slowly; yet, although the coast is by no means an
even one, a subsidence of even 100 feet would make a very great
difference in the direction that Dana has suggested. The coast,
too, of Australia inside the Great Barrier Reef certainly does not
show the characters that Dana propounded.
Saville Kent has brought forward an argument for subsidence
from the distribution of the animals, now peculiar to Australia
and the neighbouring islands. He draws attention especially
to the Darling Downs deposit in which the bird remains find their
1 Loe. cit., p. 273.
490 Mr Gardiner, The Coral Reefs of [Mar. 7,
nearest allies in New Zealand, of which one species is classed
directly with the genus Dinornis'. The deposit is referred to an
epoch not later than the early Pliocene. The time at which the
Great Barrier Reef of Australia originated is placed “somewhere
about the period of the later tertiaries.” The Rev. A. H. Cooke,
in speaking of the distribution of the land Mollusca of the
Melanesian Province, including the New Hebrides, New Caledonia,
the Loyalty and Fiji Islands, remarks that “these islands are very
probably the remains of what was once a much wider extent
of land®.” The arguments to be deduced in favour of subsidence
from the distribution of animals are worthy of every attention.
If the views of Saville Kent and Cooke are correct the origin of
coral reefs must be, comparatively speaking, either quite recent,
or the subsidences must have been very rapid and the traces of all
the former reefs have been obliterated, or, finally, the origin of
coral reefs must be put down to some other cause than subsidence.
Again, the subsidence, required by Darwin’s theory, must be
slow and long-continued to form the atolls and barrier reefs of the
Pacific. All the evidence of movement in this ocean such as it is,
decidedly points, however, to the movement as being rapid and
local. There are many local upheavals, and conversely, if local
upheavals occur, there should also be taking place in a similar
manner local subsidences. ‘The evidence does not show that these
elevations have been slow, but rather in sudden steps. I have
already given my reasons for thinking that the upheavals, which
formed the several limestone islands of the Lau Group of Fiji,
were rapid ones. The characters of the raised reefs of the
Solomon and Tongan Islands as described by Guppy and Lister
also go to show that the upheavals, which formed these, were
probably rapid. The terrace formation of Christmas Island*, in
the eastern part of the Indian Ocean and of Cuba, is not what one
would expect to find if the elevation had been slow; there would
rather be required a series of sudden upheavals with, between
these upheavals, periods of rest. Conversely there should also
have been sudden local subsidences with long periods of rest. I
have examined all the charts of the islands in the Pacific Ocean, and
of no island can I find any indication of such subsidences in the
soundings off them. Professor Bayley Balfour, in his description
of the island of Rodriguez*, mentions the existence of what he
believes to be an old reef at a depth of about 90 fathoms; it
must be remarked in connection with this that he considers that
the present reef rests on it, but whether directly, or by an outward
1 The Great Barrier Reef of Australia, p. 136 et seq.
2 Mollusca in the Cambridge Nat. Hist., p. 323.
3 Dana, loc. cit., p. 274. .
4 Phil. Trans. R. Soc., cuxviit., 1879.
1898. ] Funafuti, Rotuma and Fit. 491
extension of its talus slope he does not say. The sections of the
sea bottom off Masamarhu Island’ in the Red Sea can only, I hold,
be taken as indicating sudden and rapid subsidences.
The limestones 4,000 to 6,000 feet thick mentioned by Dana?,
with similar fossils from top to bottom, afford no evidence to show
that there have been to form them “slowly progressing sub-
sidences” of 4,000 to 6,000 feet. I do not contend that these have
not been formed by subsidence, or that the subsidence was not
a slowly progressing one, but I do protest against the too rapid
conclusions, which fix at once the nature of the bottom, and the
depth at which the organisms lived, without allowing them any
power to adapt themselves to changed surroundings and con-
ditions of life. An absolutely vertical thickness of coral limestone
of more than the 1000 feet of Vatu Vara has, as far as I know, not
yet been proved; the real thickness to the volcanic rock indeed
may be considerably less. Dana and others do not show of what
constituents the raised limestone’reefs are formed. Hence it is
purely an assumption to suppose that the whole thickness of any
of these raised reefs has been formed mainly of coral in the way
which the subsidence theory requires; there is no more evidence
that their lower parts are formed in this way than, for instance,
that they are formed by the fragments of a talus slope, which
have been consolidated together.
Dana explains the absence of fringing reefs and shoals inside
barrier reefs on the supposition that the conditions are much more
favourable for the latter than the former. “If the barrier in-
creases one foot in height in a century, the inner reef, according
to this supposition, would increase but half a foot; and any rate
of subsidence between the two mentioned, would sink the inner
reefs more rapidly than they could grow and cause them to
disappear.” According to Dana’s view, as already mentioned,
the Fiji Group forms an area, where subsidence is still going on.
It must be remembered, however, that in Fiji the land is fringed
with a reef inside the lagoons of barrier reefs, where the island
has a broad stretch of water between the barrier and itself. The
great luxuriance of the reef east of Wakaya and the volcanic part
of Vanua Mbalavu is very noticeable, and yet on the subsidence
continuing both of these are to disappear. Coral grows in the
localities I have visited far more luxuriantly inside the lagoon
than where the reef is exposed to the full force of the ocean.
Bourne remarked on the rich growth in the lagoon of Diego
Garcia, in positions where sand is not deposited, and at Funafuti
it was apparent to all the members of the first expedition
1 Nature, Xxxvi., p. 413.
IOS, | D> PRS
3 Dana, loc. cit., p. 265.
492 Mr Gardiner, The Coral Reefs of [Mar. 7,
how much more luxuriant the growth of coral was in the lagoon
than on the outer reef. Study of the charts of such islands of
the Pacific Ocean as have been surveyed and other information,
collected by me, has shown me that shoals in lagoons are gener-
ally nearly awash, and thus a conclusive proof is afforded, if we
accept the theory of subsidence, that at present the whole Pacific
Ocean must be in a period of rest. When the barrier reef is
far distant to windward, the sea may have great force within
the lagoon, the inner reef be well formed and somewhat strewn
with boulders. Yet the building-up power of the coral is so
small here, or the subsidence has been so rapid, that nowhere
are there to be found secondary barrier reefs, as it were, inside
the primary reefs. There must be other causes inside the lagoon
which prevent the formation of these, or, as I fully believe, the
constituents of a barrier reef are radically different from those of
an inner reef, which has grown up as such.
In my opinion, the effect of the waves on loose coral and shell
materials, of which Darwin supposes the reef to be mainly formed
should be noted. Dana states precisely his opinion on this point’.
It serves to “ widen the reef,” the windward reefs being the widest,
as more fragments would be heaped up by the heavier seas, the
growth also being probably greatest to windward. Yet the wind-
ward reef, including the raised islands of Funafuti, is narrower in
many places than the leeward reef, and the same is often the case
in Fiji. All the windward reefs in Fiji are of about the same
breadth, and indeed through the whole Pacific barrier and atoll
reefs to windward show a striking uniformity among themselves
in width. The material then is “to steepen, as a consequence of
the widening, the upper part of the submarine slopes.” The
sections off the barrier of Tahiti, mentioned by Murray?®, and
the sections run in 1889 by the Hgeria off Sydney and Canton
islands in the Phoenix Group, and by the Penguin in 1896 off
Funafuti? all show a fairly even slope to about 40 fathoms at
about 250 yards from the edge of the reef, and then a sudden
precipitous fall of about 75°. My own observations off the Fijian
and Rotuman reefs show the same characteristic slope to about
40 fathoms and then a sudden fall. This steep would seem to be
a feature of all reefs, rather than one due to particular reefs being
in a condition of rest in a general area of subsidence. Where the
deposits from corals and shells do not exceed greatly the loss by
subsidence and current waste “the atoll reef should lose in
irregularity of outline and thus approximate towards an annular
form.” The effect of this should be seen in the so-called “sunken”
1 Loe. cit., p. 270.
2 Dana, loc. cit., p. 282.
3 Nature, Vol. tv, 1897, p. 375.
1898.] Funafuti, Rotuma and Fiji. 493
atolls, such as the Coombe, Waterwitch and Alexa banks and
in the atoll-reefs in the Lau Group of Fiji. Some atolls too
might have been supposed to have passed through this condition,
nevertheless the study of the charts of the atoll-reefs, in com-
parison with the barrier reefs of the Pacific, has completely failed
to show in them any increased regularity of outline, or any
approach to an annular form, The smaller atolls inside the larger
atolls of the Maldive Group are of a similar character to the atoll
shaped shoals inside the Great Barrier Reef of Fiji; here the
conditions, which Dana suggests, would naturally be expected to
exist with a like effect to follow. However, I do not think that it
can be maintained that these are the effects of the debris of the
outer reefs at the present day, or have been in the formation of
the atolls of the Pacific in the past.
The reef debris would next fill the lagoon, or, failing sufficient
contributions, the atoll bank would, according to Dana, lose its
channels into the lagoon and “become at last a small bank of
reef rock with a half obliterated lagoon basin.” The observations
of Admiral Wharton are summed up on this question, when he
remarks’, “I have no hesitation in saying that a flat floor is an
invariable characteristic of a large atoll and I cannot find his
(i.e. Darwin’s) ‘deeply concave surface’ in any large atoll. On
the contrary, a flat surface is found in all these, whether the rim be
above, or below the surface.” The study of the charts of the
different islands and barrier reefs of the Fiji Group show that,
while there may be abundant shoals, the bottom between is fairly
even. The fall from the reef, and then from the shoals to the
bottom of the lagoon, is cliff-like. The depth towards the side
of the lagoon gradually lessens, and in no place which I examined,
except where the sand bank runs off the main island of Funafuti,
was this cliff absent. The bottom beyond the cliff is usually
visible and generally covered by sand. By the reef it does not
show masses of debris, nor is debris being piled up and gradually
broadening the reefs, which are awash. There are plenty of banks
known in the Pacific in all conditions of submergence and all
seem to be of true atoll-form, none occurring with “ half obliterated
lagoon-basins.” It is possible that such constructive agencies
inside atoll-reefs may be in excess of the destructive, but it is
more probable that the widening of the reef within the lagoon
takes place by the growth upwards within it of shoals, formed by
means of coral and other lime-secreting organisms, and their
gradual fusion with the reef itself; this is what appeared absolutely
to be going on, as previously stated, inside the Great Barrier Reef
of Fiji and the lagoon of Funafuti.
1 Foundations of Coral Atolls. By W. J. L. Wharton. Nature, Vol. vy,
1897, p. 390.
VOL, IX. PT. VIII. 39
494, Mr Gardiner, The Coral Reefs of [Mar. 7,
Where land is formed on the reefs of lagoons, other agencies,
such as the deposition of sand, drift, etc. come into play, and
the whole lagoon may be finally converted into land. The Ellice
Islands show the stages of this conversion, which depended largely
on the size of the atolls, and the number and depth of the passages
through their rims. Funafuti is the largest, and has six deep
passages, one of 24 fathoms, and a general depth of 25 fathoms
in the lagoon, with only a deposition of sand in one place off the
large island to windward. Nukufetau has only one ‘passage, the
depth of its lagoon is about 22 fathoms, with a sandy bottom in
most parts. Nukulailai has more land, broader reefs, no passages,
and a depth of 10 fathoms with sandy bottom. Oaitupu is nearly
all land, there being only a small lagoon with a depth of 1—2
fathoms and a narrow channel to the sea at its north end; this
island is completely covered by sand, except along the coast.
Niutau, another sandy island, has in its centre a small mangrove
swamp, which is dry at low tide. Gente Hermosa, one of the
Union Islands, is of interest, having in its centre a lagoon a few
hundred yards across with precipitous sides, a depth of 5—6
fathoms and a small island in its centre; there is also, slightly
to the north, another smaller lagoon with a similar depth; unlike
the other islands which are covered with sand, the solid rock is
here continued from the reef to the lagoons, and it is probable
that the atoll owes its land to a different mode of formation’.
There is no evidence that the channels of the atoll and barrier
reefs are filling up in Fiji, but if they are doing so, it is certainly
not by the accumulation of debris in them, but rather by the
growth upwards and inwards of corals and nullipores on their
bottoms and sides.
Lastly, the waves “accumulate on the reef material for beaches
and dry land.” Certainly in the boulder zone at Rotuma an
accumulation of this kind is going on; it is also especially notice-
able on the reefs to the south-east of Viti Levu and on the
Mumbolitha reef to the south of Ngau. Most of this debris comes,
according to Dana, from the rim and outer portion of the reef, but
even narrow fringing reefs have these parts, and yet the land they
surround does not show much debris piled up, or any extension
outwards by its means. Such an accumulation may take place
but, in my opinion, both Darwin and Dana have greatly over-
estimated the amount of the debris thrown up by the waves.
Semper, Murray, and other observers, lay great stress on the
presence in the same group off different sides of the same islands
of fringing and barrier reefs. Semper’, dealing with the Pelew
1 T am indebted for this information and much of that about the Ellice Group
to Capt. Wilson.
2 Animal Life. By Carl Semper. 1881. Chap. vit.
-1898.] Funafuti, Rotwma and Fiji. 495
Islands in particular, considered the fact of great importance,
and discussed very fully its bearing on the theory of subsidence
joined with the complicated system of up and down movements,
that would have been required under this theory to explain their
formation. For the Fiji Group Moore’ and Murray’ have already
dealt with Kandavu. Wakaya has to the west off its highest
summit (590 feet) a narrow fringing reef, but elsewhere a broad
barrier reef; the land has cliffs in accordance with this to the
west, but toward the east near the sea there is a gradual slope
of about 10°. Assuming the slope to be only 5°, Dana’s more
moderate estimate, the thickness of this reef would be 1840 feet,
and the cliff to the west, if we accept his theory of subsidence,
must have been 2345 feet high. Mbatiki, Ngau, Nairai, Ma-
kongai, Moala and Matuku, all of which are volcanic islands, slope
to the sea fairly evenly on all sides, and show every variety of
reef from a narrow fringing to a well-formed barrier. Lakemba
slopes evenly from its two central peaks; its reef to the west
fringes, and to the east is a barrier, inclosing a lagoon 5 miles
broad. The greater part of the coast of Taviuni has no reef at
all or only a narrow fringing one, yet a barrier reef lies off Vuna
to the south, and to the north-east, including also the islands of
Ngamia and Lauthala; northwards there is a regular line of shoals
enclosing an area with a depth of 40—50 fathoms. The slope
from the hills of Taviuni is in all directions very uniform, and it is
inconceivable that a subsidence of this kind of 300 feet (calculating
it only from the depth of the water inside the reef to the north),
has left no trace of any reef along the greater part of its coast.
There is no difference between the appearance of the hills north
and south of Vanua Levu, or in their rock; there is, however, a
far distant barrier reef to the north and along the greater part
of the south coast, a narrow fringing reef.
I submit that the above observations afford strong reasons
against Darwin and Dana’s theories of the structure and forma-
tion of coral reefs in general and of those of Fiji in particular.
As Dana spent three months in the Fiji Group, and had a very
unique experience of coral islands, I have given his account
more weight than that of Darwin, which has the priority.
Although it is very unlikely that subsidence has been one of
the determining features in the formation of the reefs of Fiji,
or of most of the other reefs of the Pacific, I consider that, if a
slow subsidence as is suggested, or a series of rapid subsidences,
as would be more probable, took place, barrier and atoll-reefs
would undoubtedly result, not, however, of the internal structure
as suggested by Dana. My opinion is that the growth of the
debris and sand is not so great, as Dana has suggested, and
1 Nature, xu., 1889, p. 203. 2 Nature, xu., 1889, p. 222.
39—2
4.96 Mr Gardiner, The Coral Reefs of [Mar. 7,
accepting the theory of subsidence for the moment, the wonder
would be that the atoll and barrier reefs have not greater depths
than even that of 70 fathoms found on the Saya de Malha bank,
north-east of Madagascar.
I have already, in treating of the Lau Group, referred to the
great destruction of the limestone islands, which is continually
taking place by means of the wearing and dissolving actions of
the sea water. The fact of such a solution occurring here cannot
be doubted; even in the most protected parts of the salt lake of
Fulanga, which is most completely inclosed, the rocks everywhere
show the undermining action of the sea. The narrow edge of reef
under the overhanging limestone does not extend beyond the edge
of the limestone, and is evidently also being dissolved. There are
many fallen masses of rock, and islets have slipped over completely,
while there are no growing shoals, so that it seems as if they were
being dissolved away, until they became level with the general flat
of the lagoon. Corals and nullipores do not grow in the lagoon,
and there is nothing to make up for the continual waste from
solution. Murray and Irvine’ have shown that one part of calespar
is soluble at 10° C. in something over 136,000 parts of sea water ;
three corals, taken at the same temperature, belonging to the
genera Gonastraea, Melobesia and Oculina were soluble one part
in from 12,000 to 43,000 parts of sea water. The soft limestone of
an atoll is hence probably about three times as soluble as the hard
limestone of the Lau Group, so that the formation by solution in the
middle of Fulanga of a lake 10 fathoms deep with only one narrow
tidal passage, furnishes a strong argument that solution must be
of immense importance in the formation of atoll and barrier reefs.
The experiments of Reid, quoted by Murray and Irvine’, show
that, under pressure, carbonate of lime is more soluble mm sea water
containing carbonic acid gas. He took about 1 gram of the solid
nearly pure carbonate of lime, forming the skeletons of different
organisms, and tested how much of it would be dissolved by 1 litre
of sea water, containing carbonic acid gas. His results are of great
importance, and his table may be briefly summarised :
”
Average
Experiments. Pressure. Amount dissolved.
Globigerina Ooze 4 4 tons ‘1166 grams
- 1 2 tons ‘0999 ee
ay 2 Atmosphere “057 __,,
Coral Sand 2 4 tons SPA
3 Atmosphere ‘0418 ,,
Crystalline Limestone 3 4 tons 0339.
5 Atmosphere ‘0067 __,,
1 On Coral Reefs and other Carbonate of Lime Foundations in Modern Seas.
Proc. R. Soc., Edin., 1889.
2 Loc. cit., Table xvi.
1898.] Funafuti, Rotuma and Fiji. 497
The extent to which solution has been going on is very great in
the Lau Group of Fiji; and Reid has thus shown how much
greater the action is under pressure. Given a bank at a suitable
depth, nothing further is required to demonstrate how its lagoon
has been formed; the edges being covered with living organisms
would be protected while the depth of the lagoon would be regu-
lated by the amount of decay of animal matter giving off carbonic
acid gas, by the amount of carbonate of lime deposited on its floor,
and by the extent to which the currents passing in and out of the
lagoon renew its bottom layers of water. At the same time, in
large atoll and barrier reefs, I would emphasize the importance
also of these currents in removing sand and silt. Both effects of
the current depend largely on the number, size, and depth of the
passages ; of these the depth is of most importance. Considering
how rarely a depth of over 50 fathoms is obtained within barrier
reefs, and how common depths up to that are, there is probably to
be found a mean, below which increase is greater than solution,
and above which solution has the upper hand. The lagoon of
Exploring Group of Fiji has depths up to 100 fathoms, with a
passage equally deep, to which in this particular case the depth
is no doubt due; this case, however, should be considered in con-
nection with the raised limestone islands of Lau, the reefs of which
will be treated of later.
Considering that, in Fiji, coasts can be found with no reef, or
with a broad fringing reef, or with a far distant barrier reef, and
indeed with every intermediate condition between these, and that
there are many atoll-reefs such as the Charybdis, the Horse-shoe and
the Mumbolitha, I can only reiterate Murray’s conclusions, summed
up by Professor Bonney in these words!: ‘That when coral
plantations build up from submarine banks they assume an atoll
form owing to the more abundant supply of food to the outer
margins and the removal of the dead coral-rock from the interior
portions by currents and the action of the carbonic acid (gas) dis-
solved in the water.”
“That barrier reefs have built out from the shore on a foundation
of volcanic debris, or on a talus of coral blocks, coral sediment and
pelagic shells, and the lagoon channel is formed in the same way
as a lagoon.”
As mentioned before, my opinion is that the reef is formed
rather by the growth of calcareous algze of the genus Lztho-
thamnion than by either the direct building action of corals, or
the consolidation of their fragments. Hence the formation of a
rim would be due rather to the constant replacement of the sea
water outside the reef by fresh sea water renewing the supply
1 Coral Reefs. By Charles Darwin, p. 286, 1889.
498 Mr Gardiner, The Coral Reefs of [Mar. 7,
of carbonic acid gas, than to the more abundant food supply.
Undoubtedly the better food supply would be advantageous to
the corals so that these would flourish also, but my experinents
have shown that possibly the fresh supplies of carbonic acid gas
are here too the more important factor.
My reasons have already been given for thinking that reefs are
growing outwards at about the low tide level, and the deep
dredgings off Funafuti showed that stones and fragments of coral
rest on the steep slope, while there is an area of about 250 yards
in width outside the reef before the steep commences. The uni-
formity in width of this gives evidence, I think, of the depth to
which the greatest effective wave action extends, and also gives
approximately the depth at which nullipores, the chief reef-builders,
flourish. I found at Rotuma that there is over this area, when the
tide commences to rise as well as when it is falling, a distinct
undertow from the edge of the reef. I found that if I threw a
fishing line with a heavy weight attached from the edge of the
reef it was not swept back again to me. Making a further experi-
ment by substituting a large round pebble for the lead, the whole
line of 60 fathoms was quickly drawn off its stick by the strain; it
was necessary, however, to throw the pebble a distance of about
30 yards out, as otherwise it was simply washed in at my feet. I
never repeated the experiment, but the absence of pieces of reef
debris in my dredgings from this area leads me to believe that
there is really such a backwash, which sweeps the slope clean, and
piles up the talus to form the steep.
The precipitous character of the reef towards the lagoon, and
the mushroom-shaped heads of coral are, no doubt, due to solution.
This theory implies that the reef, as fast as it is formed outside, is
dissolved away inside as these barrier and atoll-reefs are fairly
uniform in breadth. The solution forms the cliff, and undermines
the shoals; the sand at the base of the cliff represents the debris
thrown over the reef, and is in this position reformed as quickly as
it is dissolved.
The rate of growth of the reef outwards depends on many con-
siderations, foremost amongst which must be placed the depth of
the ocean floor. The reef, as it grows, has to build up its foundation,
and, until it has built up this to the requisite height, it cannot grow ~
outwards; hence naturally the reef should extend out fastest where
the slope is smallest. Again, deep currents running along the
shore would naturally clean the steep of its talus, where it projects,
and so the growth outwards should be slowest here. Thus currents
would act in such a case in opposition to the slope, and the result
would depend upon which was the stronger. The reef also should
grow faster on the side on which the current runs, as it would
constantly change the surrounding water. The waves on the
1898.] Funafuti, Rotuma and Fiji. 4,99
windward side would do the same, and, where the wind and current
are in opposition, the reef would be growing equally vigorously on
all sides, as is found to be the case in the Marshall Islands.
It is not, of course, necessary that all barrier reefs should have
gone through the fringing stage to the barrier condition. They
might equally well grow up on any bank off an island, which is
within the requisite depth for the reef-building organisms. I
believe that the Great Barrier Reef of Fiji and the reef, which
bounds the deep pool between Viti Levu and Vanua Levi, has been
thus formed. The reef round this pool is by no means complete,
and if it grew out from a fringing reef, there is no reason why it
should not be moderately so. There are, also, off the north of
Vanua Levu a large number of islands, and the line of mountains,
of which the Yasawas are the emerged peaks, appears as if it
extended round nearly in the line of the Great Barrier Reef.
Should such be the case, the double nature of this reef would be at
once explained. Indeed incrusting nullipores seemed to cover
most of the surface of the inner part. These only grow where the
water is constantly in motion, and to their protection outside from
solution the reef, I think, owes its existence. This talus theory
serves also to explain why terraces due to sudden subsidences are
not found outside the reef off islands, in the same way as terraces
are found in the raised reefs of the Solomon Islands, Cuba and
other lands.
It is inconceivable that with the elevations which formed
the Lau Group of Fiji there have not been other upheavals,
which have brought areas within the depths, required by the
reef-building organisms, but many of its atoll-reefs are probably
due to different causes. After the reefs were first upheaved, it
would take a long time, owing to the loose nature of the rock
on the outside, for the organisms to get a firm hold. The
result has been that solution has gone on outside to such an
extent, that the whole thickness of the reef almost from its
highest point to the sea level has been exposed as a cliff in
many of the islands. After the reef was formed, the base of
the island would be protected by it and its solution would then
be very small. As the reef, however, spreads outwards on its
own talus a lagoon would be formed and the solution of the
limestone would at once recommence with renewed activity.
The final result would be that the whole island would be washed
away and an atoll-reef left. It is quite probable that the atoll- —
reefs of the Lau Group, particularly the larger ones, owe their
origin to this. The Mbukatatanoa atoll-reef, east of Lakemba,
with a depth of 35 fathoms has probably been formed in this
way, and every intermediate stage from such an atoll-reef to high
coral islands with narrow fringing reefs can be found in the Lau
500 Mr Gardiner, The Coral Reefs of [Mar. 7,
Group. The following list of the coral islands with their heights
and depths will make this still clearer:
eee Depth Situation of
Name of the No. of Greatest distance lagoon islands in
Island. Islands. Height. fromland in fathoms. lagoon.
in miles.
Vatu Vara 1 1030 — _— —
Naiau iL 580 — — —
Wangava 1 350 — — —
Tavunisithi 1 200 — — —
Mango 1 670 4 2 C (centre)
Tuvutha 1 800 4 9 C
Vanua Vatu 1 310 1 2 C
Fulanga 1 260 £ 5 rim
Namuka 1 260 3 13 C
Ongea 2 300 1 12 C
Naiambo i 40) $ 3 C
Malima 2 130 14 11 C
Komo 1 270 o} 2 SE
Kimbombo 3 190 1 13 C
Yangasa 4, 390 3 19 C
Vekai 1 30 13 Leh E on reef
Aiwa 2 210 2 Le S
Vanua Masi 2 80 5 20 C
Reid Reef 3 60 4 20 C
The lagoons inside all the barrier reefs in the above list are
singularly free from shoals; this, probably, is largely due to the
fine mud, caused by the solution of the limestone, killmg the
corals by which such shoals are mainly formed, and, as it coats the
bottom, allowing few firm foundations for the larvee to fix them-
selves upon.
The elevation of Thikombia-i-ra, which was probably the last
upheaved of the limestone islands to the east of Fiji, raised with
the reef a long bank to the east. On this side there is a fringing
reef about 3 miles broad, while round the greater part of the
island no reef has as vet been formed. On the bank a number of
isolated reefs are now growing up and it appears as if a barrier
reef is being formed. A long time, however, would be required
for this to reach the surface, and so m the meantime a fringing
reef has been formed, and, the depths being favourable, is pushing
its growth rapidly over the whole bank, perhaps to form ultimately
a barrier reef in quite a different manner.
According to Dana’ “an atoll-reef without green islets, or with
1 Loc. cit., p. 356.
1898.] Funafuti, Rotuma and Fiyt. 501
but few small spots of verdure” is “probable evidence of sub-
sidence now in progress,” and the existence of barrier reefs, atolls
or submerged atolls, is an evidence of subsidence ; altogether it is
clear that Dana, with the present charts before him, would
consider that the Fiji Group is, or has been up till a very recent
period, subsiding. Support, however, is scarcely lent to this by
the broad fringing reefs especially to the south-east of Viti Levu.
At this part the Rewa river, after a tortuous course of nearly
130 miles, opens into the sea. I estimated the area of its mud
deposits and its delta at about 80 square miles, all of which would
be completely submerged by a subsidence of about 8 feet. A
small river, the Navua, has a delta of about 20 square miles, and
like the Rewa, is also largely fed by a region of soapstone;
accordingly they might be equally supposed perhaps to form their
deltas somewhat rapidly. But the Ba river in Vitu Levu and the
Ndre Keti and Lambasa rivers in Vanua Levu draining only areas
of volcanic rock would require a vast period of time to form their
large deltas. The sand flats at Wakaya, Taviuni, and Fulanga, as
noticed before, are very considerable, while by Nateva Bay and to
north of Viti Levu they are in places 1—14 miles broad; these
would only be formed in a period of rest, and their formation can
be but slow, so that they also point to the probability that move-
ments of elevation and subsidence have not occurred throughout
the whole group for a considerable period.
In the next place it is necessary to consider what are the
foundations of atolls. Here I can only emphasize still further
Admiral Wharton’s views, when he says!:—“I would venture to
suggest the cutting down of volcanic islands by the action of the
sea and that this action has a far greater share in furnishing coral
foundations than has been generally admitted.” While agreeing
mainly with these views, I do not know that the sea would have
in all these cases merely a bank of cinders and ashes to act upon;
lava might well rise to a certain height and then burst its way
out above or below the water. The lava, when it first met the
water, would probably burst up into cinders and ashes, but
beneath these a crust would form and the lava might continue
to flow’.
At the same time I consider that mounds can be, and are
being, built up to the requisite height for the reef-building
organisms by the skeletons of marine animals. But what is the
requisite height? The chief building organism is Lithothamnion,
the bathymetrical zone of which must be limited to a large degree
by the extent to which light can penetrate sea water. On this
1 Loe. cit., p. 392.
2 Geology. By A. H. Green. Part 1., 1876, p. 224.
502 Mr Gardiner, The Coral Reefs of [Mar. 7,
question Prof. Hartley says':—“The penetration of light to the
bottom of the deep sea is a possible, if not a probable, phenomenon.
It is true that in the clear waters of Lake Leman photographic
plates are affected at mid-day at no depth beyond 120 fathoms ;
but Messrs Fol and Sarasin” are led to suppose that the greater
transparency of sea water will admit of the extreme limit of
luminous rays reaching a still lower level. We have accordingly
no grounds for the conclusion that because chlorophyll has been
found at a depth of 553 fathoms, even if the pigment be produced
im situ, therefore light has not penetrated so far and has not
operated in its formation.” I do not wish to contend that the
bathymetrical limit of nullipore life is to be placed at so great
depth, but that these alge grow down to 75 fathoms was shown
by one of the dredgings made by the Penguin to that depth.
The rate of growth of all algee depends largely on the strength of
the light, for on it their power of absorbing carbonic acid gas,
and giving off oxygen directly depends. Light also is probably
an extremely important factor to many reef-building genera of
corals.
I can add nothing fresh to Murray’s account of the methods
by which mounds can be built up to the requisite depth, what-
ever that may be, but I would call attention to the fact that
the growth of corals especially contribute towards this. The
evidence, so far as it goes, shows that animals in the sea have
a tendency to collect especially on any mounds; and I do not
suppose that corals are any exception to this rule. In his report*
on Madreporaria obtained during the expeditions of H.M. ships
Porcupine and Lightning, Martin Duncan noted “that the growth
of deep sea corals is very vigorous at great depths and at low
temperatures,” and “that the present deep sea faunas contain ~
species and varieties of species of the Pliocene, Miocene and
Cretaceous deep sea faunas and offshoots of the Palaeozoic fauna.”
Only 30 species were obtained, but four colonial genera were
represented; of one, Lophohelia, Sir C. Wyville Thomson re-
marked‘ that it formed “stony copses which cover the bottom of
the sea for many miles.” Of Dendrophyllia ramea, obtained in |
the cruise of the yacht Morna, Saville Kent stated*® that its
growths “were massive and weighty as any of the most solid
branching Madrepore of the Great Barrier Reef (of Australia).”
L. F. de Pourtalés obtained® six colonial genera of corals from
1 Qn Chlorophyll from the Deep Sea. Proc. R. S. Hdin., 1884—5.
2 Sur la Pénétration de la Lumiére du Jour dans les Eaux du Lac de Genéve.
Compt. Rend. xc1x., p. 783.
3 Trans. Zool. Soc. Lond. vit1., pt. v.
4 The Depths of the Sea.
5 Loc. cit., p. 72.
6 Cat. Mus., Harvard Coll., 1871.
1898.] Funafuti, Rotuma and Fiji. 503
the plateau 50—250 fathoms in depth, which bears his name. Of
this plateau L. Agassiz says’ that it “is built up entirely by
animals now living upon its surface and constantly increasing
the thickness of the bed by. their accumulation. Large fragments
of the rock were brought up by the dredge; so that its structure
and characteristic remains of animals could be studied at leisure.
I do not know that there is on record a more direct illustration
of the manner in which mountain masses of calcareous deposits
have been accumulated on the bottom of the ocean.” This rock
it must be observed Agassiz compared to the coral rag in the
Jurassic. Agassiz speaks also of the abundant fauna of this
plateau, one remark, “the variety of marine plants does not keep
pace with the variety of marine animals,” being of interest as
indicating that some plants at any rate were found all over this
plateau.
I have shown sufficiently by these few quotations, how banks
may grow up to the requisite height for the reef-building nulli-
pores. In the tropics corals would grow more vigorously and at
greater depths on account of the abundance of food and probably
the greater intensity of the light than in the temperate zone,
where the pelagic life is not so rich. That reefs are not formed
in the temperate zones is due, in the first place to solution, in
the next to the inability of the reef-building nullipores to live and
flourish in these temperatures; these algze require moreover a
strong and direct light, and such light can only be obtained at
considerable depths in the tropical regions.
These few remarks, which I have made, are intended to apply
more particularly to the coral reefs of Fiji, as well as generally
to those of the Pacific and Indian Oceans. I would not wish to
apply them to the Florida Reefs and other reefs in the West
Indies, where I think the conditions of formation were radically
different; the formation of the Great Barrier Reef of Australia
may probably be explained in a similar way to that by which
L. Agassiz has-explained the Florida Reefs. Each step in the
formation of atoll and barrier reefs, as I have tried to sketch
it, cannot, I fear, be applicable to all atoll and barrier reefs.
Nevertheless the main outlines will, I believe, be found to be
correct for most of the so-called coral reefs, but each group of
islands and each reef should be considered by itself in relation
_ to the known meteorological and biological conditions of its region.
1 Report on Deep Sea Dredgings in the Gulf Stream. Mus. Comp. Zool., 1870.
504 Mr Walter Gardiner, Methods for the Demonstration [Mayv. 7,
(2) Methods for the Demonstration of “Connecting Threads”
mm the Cell Wall. By WALTER GARDINER, M.A., Clare College.
(Received 7 March, 1898.)
I HAVE already published in the Proceedings of the Royal
Society’ a brief account of a new method for demonstrating the
“connecting threads” which traverse the walls of plant cells.
In the present paper I propose to make some further remarks
upon that method, which may be called the “ Kolossow-Safranin
method,” and also to describe a second means of investigation,
which may be briefly described as the “lIodine-Acid-Violet
method.”
A. The Kolossow-Safranin Method.
1. Killing and swelling. In this method the two processes
are accomplished simultaneously either with watery Picric acid,
Picro-sulphuric acid or Picro-acetic acid, and in certain cases with
Sulphuric acid. With refractory tissue, treatment with Picric acid
may be supplemented by that of Picro-sulphuric acid. Picro-
acetic acid was used with success in the mvestigation of the
tissue of ferns.
2. Hiaing, is effected with Kolossow’s mixture of Uranium
nitrate and Osmic acid, either of normal strength or diluted with
once or twice its own volume of water. Hermann’s mixture also
gives good results, but Flemming’s mixture and fixatives con-
taining chromic acid were found to be unsuitable.
3. Preservation. After fixing, the material may be preserved
(apparently indefinitely) in a solution of Thymol water containing
‘5 grms. Thymol to 1 litre of water, and sections may be taken as
required.
4. Staining, is accomplished either with a saturated aqueous
solution of Safranin or a similar solution containing 2°/, alcohol
and 1°/, aniline. The sections after washing in water are treated
for some time with a 2°/, solution of orange G., which dissolves
the dye from the cell wall and leaves the protoplasm and con-
necting threads stained. The threads may now be further stained
by substitution. In this direction Gentian violet gives generally
the most satisfactory results, especially if Gram’s method of
intensification be employed. Staining with Gentian violet (as
with Safranin) affects the whole tissue, but the dye may again
be removed from the cell wall by the action of a 5°/, solution of
acid fuchsin. In certain cases, e.g. the endosperm of Hordeum
1 Gardiner. Roy. Soc. Proc., Vol. xx11. 1897.
2 Kolossow. Zeit. f. Wiss. Mik., v.1. 1888.
1898.] of “Connecting Threads” in the Cell Wall. 505
vulgare, substitution of the Safranin by Eosin is advantageous,
and for many ferns Poirier’s orange may be similarly employed.
In some instances I have used Cyanin with favourable results,
5. Mounting. The sections are placed in dilute glycerine and
then transferred for permanent mounting into glycerine jelly.
Some observations on the rationale of the method may now
follow.
As regards the Picric acid no more need perhaps be said than
that the lethal action of this quickly penetrating reagent upon
the protoplasm is a well-known matter of experience, and that
living tissue exposed to its poisonous influence rapidly succumbs.
Besides killing the tissue, it swells the walls. This swelling of
the cell wall seems to me to be essentially a phenomenon of
hydration, and it is possible that the protoplasm is similarly
affected. The action of Sulphuric acid is not unlike Picric acid
itself, and possibly Acetic acid also belongs to the same category.
Certain of my experiments appear to indicate that both Picric
acid and Acetic acid function as mordants both for Safranin and
Gentian violet, though in view of the great solubility of both
reagents and the comparative readiness with which they may be
removed from tissues by washing, the real explanation may be
that cytoplasm or cellulose after having been submitted to these
actions has a much greater affinity for the two dyes than before.
At the same time it must be remembered that Picric acid gives
a precipitate both with Safranin and Gentian violet.
Kolossow’s mixture is a far more deadly poison than Picric
acid; is exceedingly rapid in operation ; and fixes the tissue with
little or no change. It also hardens the structures and makes
them very favourable for cutting and subsequent manipulation.
Unlike Picric acid there seems to be no question of hydration
here, and the action of both the Osmium and Uranium salt
appears to consist in forming a fixed and insoluble compound
with the tissues exposed to their influence.
From the point of view of staining it is the Uranium which
plays the more important part in that it and not the Osmic acid
acts as a mordant to the Safranin. In the case of Hermann’s
mixture it is the Platinum salt which performs a similar function,
The Uranium on the other hand does not mordant Gentian
violet, and no satisfactory results can be obtained by staining
with Gentian violet direct. Thus the staining has always to be
effected through the intervention of Safranin, which with this
particular method must be taken as the starting point of all
further treatment.
It must not however be imagined that this fact constitutes an
objection to the use of Safranin. Safranin is on the contrary
almost an ideal dye for such an investigation as the present,
506 Mr Walter Gardiner, Methods for the Demonstration [Mavr. 7,
and any tissue which can be stained with it, admits of very wide
treatment on account of the numerous and important substitu-
tions and combinations which can be subsequently effected.
In connection with the Safranin method it is important to
note that it is the protoplasm and connecting threads which
appear to be mordanted by the Uranium, and that it is in these
structures that the precipitate of Uranium and Safranin which
cannot be dissolved by the Orange G. is formed.
B. The TIodine-Acid-Violet Method.
As the Kolossow-Safranin method depends upon the fact that
the Uranium salt in combination with certain elements of the
dead cytoplasm acts as a mordant to the Safranin, so in the
Todine-Acid-Violet method, the Iodine is the mordant and an
Aniline violet the dye.
We owe to Meyer’ the latest ssposteion of the relations between
Iodine and certain of the Aniline violets, as well as the explicit
account of an excellent method, for the demonstration of “con-
necting threads.”
Meyer brings clearly into prominence the part played by
Iodine as a mordant, and to him belongs the credit of stating
with precision the great importance of this fact and dwelling
upon the significance of it in connection with his method.
His method is as follows:
Sections of fresh tissue are treated with a solution made by
adding *5 grms. Iodine and ‘5 grms. Potassic Iodide to 100 cc. of
water. They are transferred to a slide together with a small
_ quantity (a half drop) of the Iodine solution. One or two drops
of a 30°/, solution of sulphuric acid saturated with Iodine are
added and the cover-slip is put on.
Then a half drop of a 3°/, solution of Pyoktanin is run
under the edge of: the cover-slip. The Pyoktanin is at once
dissolved by the sulphuric acid, forming a brownish yellow or
greenish yellow solution which, together with the Iodine present,
stains the protoplasm and the “connecting threads” black. The
various details of staining may be observed under the microscope.
After some three minutes have elapsed the slide and its contents
are placed in a vessel containing about 400 c.c. of water. In
successful preparations the cell wall is stained light blue and
the protoplasm and “connecting threads” blue black. The fine
precipitate formed by the union of the Iodine and Pyoktanin,
which is frequently deposited upon the section, may be removed
by brushing.
The author made a series of observations upon the aniline
1 Meyer. Besichte der Deutsch. Bot. Gesell. Bd. xv. Heft. 3. 1897.
1898. ] of “Connecting Threads” in the Cell Wall. 507
violets suitable for the above reaction, and has found that the
methyl violet manufactured by Merck and known as Pyoktanin,
(a chlorhydrate of pentamethyl and hexamethyl pararosanilin)
gave the best results.
I may add that Gentian violet gives almost (if not quite) as
good results as Meyer’s Pyoktanin.
Meyer’s method has lately been used with success by Kohl" in
demonstrating the “connecting threads” in the epidermal cells
of Viscum album and in the parenchyma cells of the “leaf” of
Mnium undulatum and other mosses.
On repeating the experiments of Meyer it is easy to see that
the method is an admirable one and is a great advance upon any
of the analogous methods which have preceded it. Moreover
Pyoktanin has excellent staining powers and constitutes a reagent
of the first rank for investigations of this kind.
Meyer’s method has however certain drawbacks, which become
apparent when actual experiments are made, and they may be
summarised as follows.
1. Want of delicacy and control.
2. Want of certainty and uniformity of results.
3. The formation of the Iodine-Methyl-Violet precipitate.
4. The use of fresh tissue.
One finds in practice that it is difficult to arrange with certainty
that the union of the Pyoktanin and Sulphuric acid shall take
place in the neighbourhood of the section, and even when this is
accomplished, the varying proportions of the acid and the dye
may end in the formation of either a propitious or unpropitious
mixture, which in consequence may or may not stain in the
proper manner. The somewhat voluminous blue-black precipitate
which accompanies the union of the two liquids is an impediment
to observation, and too frequently a group of granules appears at
the identical place one wishes to examine. The results produced
by the final treatment with water are by no means uniform, and
one has frequently to perform the whole process over again.
Finally the use of fresh material involves the possibility of
structural changes during the cutting and manipulation, as well
as inability to be independent of times and seasons.
The chief drawbacks to which I have alluded are not uncon-
nected with the fact that the various operations of killing, fixing,
swelling and staining are carried on simultaneously. In the
modification I am now about to describe these operations are
conducted apart, so that the whole process involves several
separate stages, and each stage can command its own special
1 Kohl. Bot. Central. Bd. uxxu. No. 8. 1897.
508 Mr Walter Gardiner, Methods for the Demonstration [Mar. 7,
treatment. By this means also the rationale of the whole process
is considerably elucidated.
(1) Killing and fixing are in all cases brought about by means
of Iodine. Small pieces of tissue are treated either with Iodine
water or more usually with a solution of Iodine dissolved in
Iodide of Potassium. For delicate tissues of small bulk a strength
of ‘1 or ‘2°/, Iodine in ‘15 or °25 °/, Potassic Iodide in water is
sufficient, but for the average tissues a solution containing ‘5 °/,
Iodine in ‘75 °/, Potassic Iodide in water is necessary for rapid
penetration. The tissues may either remain in the Iodine solution
as required for cutting or may be preserved in a solution of
Thymol water.
(2) Swelling. Sections having been cut in water are swollen
in sulphuric acid. The strength of the acid employed is essen-
tially dependent upon the character of the tissue; 1—5 °/, bemg
sufficient for such tissue as that of Chara or the “leaf” of Mniwm
undulatum, 5 °/, for Viscum album and 30 °/, for Aucuba Japonica.
Solutions contaiming Picric or Acetic acid do not give satis-
factory results. My experiments appear to show that sulphuric
acid is for this particular method the swelling agent par eacellence.
(3) Staining. The sections are first mordanted with Iodine.
To this end they are treated for a short time with an Iodine
solution in 5°/, sulphuric acid. The Iodine solution may contain
either 5°/, Iodine in °75°/, Potassic Iodide, or 1°/, lodine in
1:25 °/, Potassic Iodide. Meanwhile the staming mixture is
prepared, and must be freshly prepared for each occasion. Two
stock solutions are made up. The first is a 10°/, solution of
Sulphuric acid and the second is a ‘5 °/, or 1°/, solution of
Pyoktanin or Gentian violet in water. The staining solution is
prepared by mixing equal parts (say 5 cc.) of each, so that what
is produced is a ‘25 or 5°/, solution of the Violet in 5°/,
Sulphuric acid. A sufficient quantity having been poured out
into a watch-glass, the sections are taken out of the acid Iodine
solution, quickly passed through a solution containing ‘1 °/, Iodine
and ‘15 °/. Potassic Iodide in 5 °/, Sulphuric acid, and then placed
in the solution of acid Violet. After some ten minutes have
elapsed they are taken out, and washed freely in water and may
be forthwith examined.
(4) Intensifying. If the swelling and staining have been
properly conducted it will be found that the protoplasm and
“connecting threads” are stained blue, and that the cell wall
remains almost uncoloured. It is however a great advantage,
and frequently a necessity, to make the staining much more
pronounced, so that the threads may be the more easily observed.
1898. ] of “Connecting Threads” in the Cell Wall. 509
This may be done either by means of Iodine alone, or by repeating
the operation of mordanting and staining one or more times.
Intensification with Iodine is accomplished by simply treating a
stained section either with a solution containing ‘1 °/, Iodine and
15 °/, Potassic Iodide in 5 °/, Sulphuric acid, or with a solution
of 5°/, Sulphuric acid saturated with Iodine and then examining
the section mounted in one of these reagents. The Iodine forming
a black precipitate with the Aniline violet causes the protoplasm
and threads to stand out much more clearly than before. The
blue tint assumed by the cell wall in consequence of slight °
staining also disappears, since the Iodine in virtue of its intense
affinity for the Violet combines with every trace of the dye.
When intensification by staining is desired the tissue is
mordanted with an Iodine solution, which should be more dilute
than on the first occasion of staining. It is then passed through
a 5°/, solution of Sulphuric acid and again treated with the
Sulphuric acid solution of Gentian violet or Pyoktanin. If
again treated with and examined in dilute acid Iodine, the proto-
plasm and the threads stand out intensely black and peculiarly
clearly. One should mention that when secondary staining is
resorted to, a certain amount of precipitation upon the section
may occur which may necessitate the use of a brush before
examination.
(5) Mounting. In order to render the violet stain “fast,” I
mount in glycerine containing a small percentage of Zinc chloride,
and still better results may sometimes be obtained when a trace
of Iodine is present. The Zinc chloride acts in virtue of its
property of forming a dense blue precipitate with Gentian violet
and Pyoktanin. The mounting solution may be made as follows:
oa c.c. Glycerine, 60 c.c. of water and 10 cc. of a 20 */, solution
of Zine chloride are mixed together. To this 1s added a flake or
two of Iodine and the whole is shghtly warmed over a warm bath.
Section: may be transferred from the above solution into Glycerine
jelly.
The demonstration of “connecting threads” in such structures
as the “leaves” of mosses and the like, where the whole organ is
implicated and the cutting of sections is either undesirable or
difficult, involves considerable modification of the above treatment
and is not unattended with many manipulative troubles, by reason
of the fact that it is exceedingly difficult to limit the staining to
the protoplasm and threads, and to prevent it extending to the
walls.
Successful results appear to depend upon the use of low
percentages of Iodine for the killing and still lower for the
mordanting. For the swelling I find that a 5°/, solution of
sulphuric acid is sufficient. As the result of an elaborate series
WAOIb, IDS, 4, WAGEE 40
510 Mr Walter Gardiner, Methods for the Demonstration [Mav. 7,
of experiments I also find that if the swelling is followed by
treatment with a dilute solution of sulphuric acid containing a
trace of Potassic permanganate the walls are: bleached, and at
the same time so altered in character that after mordanting they
no longer stain with the acid Violet, and thus the threads are
brought very clearly into view. The threads may be readily
demonstrated at the edges of the preparation by means of the
ordinary technique when due regard is paid to the special require-
ments already mentioned. The complete absence of threads from
the external walls is very striking, and still more striking is the
enormous number of the threads present.
It now remains for me to make a few concluding observations
upon the rationale of the Iodine-Acid-Violet method.
The great merit of Meyer’s modification is, as I have already
remarked, that it places in the foreground the important réle of
the Iodine and makes definite provision for mordanting ‘the
protoplasm and threads before the application of the dye. This
was not done by earlier observers, although I quite agree with
Meyer in thinking that what success attended the somewhat
analogous methods of Russow’, Terletzki?, Kienitz-Gerloff?, and
(I may add) Poirault*, was not unconnected with the fact that
at the time of staining some traces of Iodine were present in the
tissue.
The same is possibly true of the Iodine-Chlor-Zinc-Iod-
Aniline-Blue methods of Russow® and myself®.
The mordanting properties of Iodine in combination with
Aniline dyes has of course been long known, having been used
in conjunction with Gentian violet by Gram’ in 1884 and
Bizzozero® and Nissen” in 1886; and I see from my notes that
I have myself used it since 1895 in connection with my Kolossow-
Safranin method. These facts however in no way detract from
the excellence of Meyer’s own researches.
The mordanting properties of Iodine appear to result from
the remarkable and phenomenal manner with which it is taken
up by the protoplasmic structures of the cell.
It is difficult to frame any adequate explanation of this
interesting fact, and the very expressions one uses in connection
with it must, I fear, be but vague and unsatisfactory. No
1 Russow. Sitzber. der Dorpat. Naturf. Gesell. 1883.
2 Terletzki. Jahrb. f. Wiss. Bot. Bd. xv. 1884.
3 Kienitz-Gerloff. Bot. Zeit. 1891.
+ Poirault. Annales de Sci. Nat. Bot. 1893.
> Russow. Sitzber. der Dorpat. Naturf. Gesell. 1882.
6 Gardiner. Phil. Trans. Roy. Soc. 1883.
’ Gram. Fortschr. d. Medecin. 11. No. 6. 1884
8 Bizzozero. Zeit. f. Wiss. Mik, 11.1. 1886.
Nissen. <dArch. f. mik. Anat. 1886.
Cc
1898.} of “Connecting The--ds” in the Cell Wall. 511
doubt the phenomenon is partly one of simple diffusion, and
results from the circumstance that diffusion into the protoplasm
is easier than into the refractory and markedly mucilaginous cell
wall. But in addition to this simple diffusion there also appears
to be a definite selective affinity between the Iodine and the
dead protoplasm, which stated more philosophically is in reality a
chemical affinity, as is also in a smaller degree diffusion itself.
But be this as it may, the extraordinary rapidity with which
mere traces of Iodine are absorbed by the protoplasm and the
threads is almost beyond belief.
The precise manner in which the Iodine travels from cell to
cell is not quite clear, but in certain instances I am led to believe
that it is vid the threads rather than vid the walls.
Not less important than the relations between the protoplasm
and its mordant are the relations between the mordant and its
dye, but all that one need say on the present occasion is that
Iodine and many of the Aniline violets have an intense affinity
the one for the other, and that even in the most dilute solutions
where only traces are present the characteristic precipitate which
plays so important a part in the Iodine-Acid-Violet method is at
once formed,
A second and almost equally important factor in the success of
the method is the part played by the sulphuric acid as the solvent
of the Aniline violets; and in this connection two points especially
deserve notice, viz. (1) that the dye when first dissolved in the acid
exists 1n a very perfect state of solution, and (2) that upon solution
the tinctorial properties of the dye become profoundly modified.
As to the first pomt it will be found that watery solutions
of the Violets penetrate into tissues with some difficulty, but that
alcoholic solutions, and especially solutions in acids, are much more
readily diffusible.
The second point is however much the more important, and it
is this; that Gentian violet or Pyoktanin when dissolved in
sulphuric acid stains the protoplasmic structures only and ceases
to colour the cell wall. That this is so may be easily demonstrated
by the following experiments, A and B.
A. (1) Sections of normal tissue having been treated with an
aqueous solution of the Violet—the cell wall and protoplasm are
both deeply stained.
(2) Sections of tissue having been swollen with sulphuric
acid and washed and treated with an aqueous solution of the
Violet—the results are practically the same as before.
B. (1) Sections of normal tissue treated with a ‘5 °/, solution
of the Violet in 5 °/, solution of Sulphuric acid—the protoplasm
is stained but the cell wall hardly at all.
512 W. Gardiner, Methods for the Demonstration, etc. [Mar.7, 1898.
(2) Sections of swollen tissue treated as in B. (1) give a
result practically the same as B. (1).
It is not the alteration in the cellulose produced by the acid
which determines the reaction, simce experiment shows that a
swollen wall can be subsequently stained by an aqueous solution
of the dye; neither is it necessarily all acid solutions which produce
the result since when the dye is dissolved in acetic acid a sensible
staining of the wall occurs.
As regards the relations between the dye and its solvent, the
following points deserve notice.
A freshly made solution of Pyoktanin or Gentian violet con-
taining ‘5 °/, of the dye dissolved in a 5°/, aqueous solution of
sulphuric acid is at first of a vivid green colour with a yellowish
tinge. The colour however soon commences to fade, and after
some time entirely disappears. For a short period this liquid
would appear to conta a solution of the dye as such, but
decomposition soon commences and ends (I presume) with the
formation of a colourless sulphate of the base. Whether the
sulphuric acid may at any time be regarded as containing un-
altered Pyoktanin or Gentian violet, or whether at the moment
of admixture a chemical change occurs must for the present be
left an open question, but one salient fact becomes obvious, viz.
that the staining powers are greatly diminished and bear little
comparison to those exhibited by the dye when in aqueous
solution. Further, such staining as does take place is fairly
limited to the protoplasm.
The selective characteristics of the Acid violet are naturally
accentuated by the use of Iodine, since the Iodine itself has
analogous affinities for the cytoplasm and threads, and has in
addition an intense affinity for the dye.
That the mordanting action of the Iodine is mainly limited to
the protoplasm may also be proved by the following experiment :
A section is swollen with acid and washed, and is then treated
with Iodine and stained with an aqueous solution of one of the
Violets, when it will be found that both the protoplasm and the
cell walls are deeply stained. If now placed in a 5 °/, solution of
sulphuric acid the dye is dissolved from the walls but not from
the protoplasm, so that both the protoplasm and the threads come
into view.
As this paper is concerned with methods only, I do not
propose to give an account of my more recent results, but my
work in this direction is proceeding and will be published in due
course. I also intend to deal with other modifications of the
two methods I have now described.
PROCEEDINGS
OF THE
Cambridge Philosophical Society.
Monday, May 2, 1898.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
At a Meeting of the Society held at the Cavendish Laboratory
the following were elected Fellows:
J. Stanley Gardiner, M.A., Gonville and Caius College.
W. F. Sedgwick, M.A., Trinity College.
The following Communications were made to the Society :
(1) On the theory of Order. By E. T. Dixon, M.A,, Trinity
College.
All the theorems of non-metrical (projective) geometry depend
solely on the conception of “ order” so defined as to be independent
of the idea of “before and after,” which belongs only to Time. It
follows from this definition that no “order” can be ascribed to less
than four units in any uniform group; and this is why less than
four points have no “ projective relation ” or anharmonic ratio. The
paper further discusses the way in which numbers (or coordinates)
may be assigned to the units of a group for purposes of analysis,
with or without a system of “unique” lines having already been
determined.
(2) On a certain system of differential equations defining ,
periodic functions*. By H. F. Baker, M.A., St John’s College.
(1) Suppose we have a consistent system of differential
equations
PU a ()
OUjOUjOUZOU RL On Us)’
* [21 September. The contents and the title of this note have been modified
since it was presented to the Society.]
WO, IDS, Ie, Wanne. 41
514 Mr Baker, On a certain system of [May 2,
expressing that partial differential coefficients, of the dependent
variable w, of the fourth order, are rational functions of the
partial differential coefficients of the second order, neither the
partial differential coefficients of other orders, nor the independent
variables uw, u,,..., entering explicitly. For definiteness suppose
there are three independent variables; then the greatest possible
number of equations is fifteen, and the rational functions contain
six partial differential coefficients of the second order. If we
differentiate the equations once, and eliminate the resulting
differential coefficients of the fifth order between pairs of the
equations, we shall obtain at most twenty-four equations, each
linear in the ten partial differential coefficients of the third order,
the coefficients of these bemg rational in the differential coeft-
cients of the second order. The elimination of the differential
coefficients of the third order, which we suppose to be possible,
will then lead to rational relations connecting the differential
coefficients of the second order. We suppose that these rational
relations are algebraically equivalent to as many as there are
independent variables, namely three, which we may denote by
fi(&, Y, 4, é, Up o)= 0, A(@, Y; 2; 3 1; ¢)=0, f(a; Y; 4; é, Up €)=0,
where #, y, 2, &, n, € denote the partial differential coefficients of
the second order,
Ow Ow Ow nw Ow Ow
. Ott?” J ~ ulg0Us eT BundU,? © Ode? as, Up,” > OUg?
In the course of deducing these three rational equations we
shall obtain such equations as
OD GD) aap
Pou? Q dusdu, BR du20uy,
IRR GHAD St ll GUNN RRCUD
7 P, du,du2 Q, dusdu,du, © Ry ougoue? 97
where P, Q,..., A,,..., are definite rational functions of a, y, 2,
—,m, ¢ Putting each of the fractions equal to ~ we have
Ow 4, Ou A /GIP oP oP oP oP _
pa a a a, One Oe ge, ed
oy _ 9 dQ pine), Fe aes, hed :
Ayn a we Ge P+ aye de ee os Qi + ay 3
hence, replacing the left sides by their rational expressions
Mee
Wises: (a, Yy, a, S 1; S)) Resgeo (a, Yy, Z, & 1), g), and eliminating aie ue
and can hence
obtain w? as a rational function of a, y, 2, & 7, €
1898.] differential equations defining periodic functions. 515
express the partial differential coefficients of the third order in
terms of a, y, z, & 7, § in the forms
o*w
Ou,?
where P and p? are rational in a, y, 2, &,7, & We obtain several
different forms for uz? in a similar way. It is supposed that the
differential equations are such that these are algebraically
equivalent in virtue of the equations f,=0, L=90, f,=0.
= “P, etc,,
Now we have
OFw
Ow
AU
Oug? Aus ;
re du, = nw (Pdu,+ Qdu,+ Rdw),
Jt
2
3,
7 3 i du, + =
OUus* OUs
and similarly,
dy = p(Qdu, + Pidu,+ Qdu), dz = w(Rdu, + Qidu, + Rk, du) ;
thus we have
w= | (Ade + Hdy + Gdz),
n= [7 (Hae + Bay + Fae),
m= [| Gde + Fly + Cae),
where A, B, C, F, G, H. uw? are rational functions of 2, y, z, & , &
these latter being connected by the rational equations /, = 0,
ple K—6.
Therefore, if the original differential equations have a
solution of which the second partial differential coefficients are
single-valued functions, these integrals will be capable of inversion,
and define x, y, 2, &, n, € as single-valued, in general simultaneously
periodic, functions of uz, U2, %. Whence the solution of the
differential equations can be completed.
In what follows we obtain systems of differential equations of
the form just considered, the system with p independent variables
being satisfied by all hyperelliptic theta functions of p variables,
independently of the characteristic of the theta function (the
dependent variable w being the negative logarithm of the theta
function), and we verify in detail for the cases of two and three
variables that the necessary conditions for the application of the
method of integration sketched above are satisfied. The method
would appear to be of importance as an elementary introduction
to the theory of theta functions, but it has a wider application,
namely to the general theory of functions with simultaneous
period-systems.
41—2
516 Mr Baker, On a certain system of {May 2,
(2) Let
o(u)= > evet Qriv (a+r) + int (ntry + 2miq (n+7)
Ny... Np
be, as usual, the general hyperelliptic theta function of p variables,
with any characteristic, the quantities a occurring in the quad-
ratic form au satisfying the equation
e ate a fz Dy: vg
Wagyu uj? = 1 | dadz 2ys + F («, 2)
e ade VS 4A(a@—zyP ”
wine’ IN, 2) = Dir (A y= as E F(a, )| = £ f(@) 5
Po. 0?
further let @,j (uw) =— a) logo (U), ijn (Uv) = POs Qi; (w),
and let @,, @, és, é, be any quantities whatever.
Then we have the relation
8 (2 — €3) (¢3 — €1) (€ — &2) (€4 = €1) (24 — 2) (24 - €5) nee Orv (u) - oh het eee
Hee) G)IEM een Be) <All =a (9) aera
LF (e4, @) — 4 (e,- 4)? a Q,,, (0) ei Relea
+ (€3 — €) (€4— @o) [F' (es, &1) — 4 (e3 — &1)? oe P,, (w) Ee
[LF (¢4, €2) — 4 (@4 — &2)? ae Pru (u) ete |
+ (€, — €2) (€4— es) [F'(e1, &2) — 4 (@ — e2)? ae Pru (u) eeu
[F (e4, ¢3) — 4 (e — ey) Be @,,, mer reh—*],
wherein
zee Zz pil dy i p
u; = » P =f (#) =(&, Vopr, UW = TUG,
a y r=1
and F(a, z) may have its most general form. The summation for
each of the symbols X, pu, v, p is from 1 to p.
The deduction of the explicit forms of the differential equa-
tions, by equation of like powers of @, é2, é;, @, on the two sides,
is a question in the calculus of symmetric functions.
(3) For the case of 2 variables we put down the differential
equations in two forms, (a) the explicit form, in accordance with
§ 1, (8) a symbolical form, itself of some interest.
* Compare, e.g., Math. Annalen, wu. (1898), p. 471.
1898.] differential equations defining periodic functions. 517
(a) Putting
SF (&) = No HA A gd” + gt? + Age + Age? + Age’,
GZ) — > x2" [Qroi + Aviyi(# + 2)], with A, = 0,
i=0
and Qx=2, On =Y, Ou = 4,
the equations are
I
—2( @2222 — 6@.)
AyAg — FAsA; — ZAWH — 2DAsy + GOAGZ
— 2 (P21 — 620) = ¥uAv —2ryyyt Az
— 2 (xn — ae = AG NG — Ay
— 40,
— 2 (Yan — 6Gu@n) = yArs + Aye — 2uy
— 2 (@un — 69%) = Apds— FAAZ+ GAge — yy — 2Az,z,
which take a still simpler form when we put r= 0, A; = 4, as we
may do without loss of generality. By differentiating the first
equation in regard to w,, and the second in regard to u,, and sub-
tracting, and acting similarly for the other pairs, we obtain four
equations, of which, for instance, one is
<a 2Y Pox ta 20 om + 2 son a Nein = 0,
and thence by elimination we obtain
— By 2x IX; =, | =0)
22 2y+tr, —(4e+4r,) 4A;
tr, —(424+2) 2y + dr; 2a
= ro $m 2z — 2y
which geometrically is a transformation of the equation of the
sixteen-nodal quartic surface first found by Gépel and considered
by Kummer. The nature of the transformation is best described
geometrically—suppose A; = 0, A; = 4, and use the abbreviations
1 F(, ¢c)
4 (b—c)’
then, if ¢,, a, C:, , ¢ are the five roots of the equation f(«) = 0,
and P denotes the plane at infinity, the sixteen nodal points are :
Pi,=ytbe—b, Py =2z+(b+e) yt bea — ec, c=
I. The infinite end of the axis of z, through which pass the
six singular tangent planes
B) 2) .
bee, Pal; Be, Pe Pe ae
518 Mr Baker, On a certain system of [May 2,
II. The five points lying on the plane at mfinity given by
where b is any one of ¢, a, C, ds, ¢, the singular tangent planes
which pass through this point being
EP, JP yy LPG Je JP ite eae
where 0,,..., b, are the four of the set ¢, a, C:, ds, ¢ other than b;
s
III. The ten points given by
i b; Te b., y= b,b., 2 = €b,, de>
where 6,, b, are any two of ¢,, Gd), C:, M2, c, the singular tangent
planes which pass through this point being
DB) D)
Py, JE. Jee L b3D4> eer I b3b5?
where b;, b,, b; are the three of the set ¢, @, ¢, a2, ¢ other than
1) b..
Still supposing A,=0, A, = 4, the expressions for the partial
differential coefficients of the third order in terms of a, y, 2,
referred to in §1, can be taken so that the squares and the
products of twos of Qo», @m, Mer, Mim are rational integral cubic
polynomials in a, y, z. I have obtained the ten equations, of which
for instance three are
Qoon = No + Ag + Aye? + 4a? + day + 42,
Qon = No + Ay? + Aay? — 4yz,
2 Orm(Oon = a + Asy + 2r.LY + Bary + Ay? — az.
The first of these equations shews that all the functions @,
@on, Qo, Yim can be expressed rationally in terms of the three
&= On, Y= On, €=@om, (a remark easily generalisable to higher
values of p). It is known that there exist cubic surfaces touch-
ing the sixteen-nodal quartic surface along sextic curves ; denoting
the right-hand sides of these equations momentarily by X, Y, Z,
the equation of the quartic can be put into the form
AX VY = Z?,
which shews that each of the cubic surfaces X, Y touches the
quartic along a sextic curve lying on Z=0. There are also
irrational forms for the equation of the quartic; for instance one
arises from the verifiable identity Qs = QxQ@o2— xP: Further,
in the form ?=¥ (a, y), to which the equation is reducible bi-
rationally, y (a, y) is the product of the five expressions Pp.
1898.] differential equations defining periodic functions. — 519
The expressions for uw, u as linear integrals can now be
obtained as in § 1. The result can be brought into a familiar form
ae 3 ean
? Li STAN
ee aw
0g 0g
where Y=0 is what the equation of the sixteen-nodal quartic
becomes when we substitute for z in terms of a, y and €, where
€= @.,, and L, M, N are rational integral polynomials Tih yy 1G.
From the point of view of the theory of functions it is the surface
V=0, rather than the sixteen-nodal quartic, which is to be
regarded as fundamental.
(8) Coming next to a certain symbolical form of which the
differential equations are capable, we notice that we have
2
Ca a Ze 3 Aico’, Qn = — = A,A,oo'’, Qu =— = Aico’,
and similarly
Qo — 602 —— OO 2202 — ee atk Bom =— = Aico’, etc.,
where
Shy 0 CoN a
Mas = (= _ = o (Uy, Uy) a (Uy, Uy ), etc.,
the variables w,’, ws’ being replaced after differentiation by a, ws.
Now let k., k,, %, w, , m be arbitrary constants, let us take .
Klein’s invariantive form for the polynomial F(a, z), and
Eve [ Art p)de xa =| "2 + pw’) dx
Oy = ee ee
Ve a NGS
then the differential equations are summed up by
1 0 @ ae iil aga
3 | (& Ov, + le; =) Coxe @ dvs s= k, 5a”) | oo
= (Au — Np). (db ) bith, oo"
= i ZN?) ht oO = oO 0 = 0 ) gee
Ow’ =n). $5] (55, bezy) — (bean Sane) | 2m
where o is regarded as a function of v,, v,, and, after differentiation,
V2, ¥, are to be replaced by 2, %.
d= bik, + ok, = <
This form shews, by equating terms of the same dimension on
the two sides, that the equations can be used to obtain the expan-
sion of the o-functions in integral powers of the arguments, and
gives an immediate proof of the known theorem as to the
invariant and integral character (in the coefficients of $%) of the
520 Mr Baker, On a certain system of [May 2,
terms; as a practical example I have obtained the expansion of
the function o,(%, U2) up to terms of the ninth order, assuming
only the terms of the first order to be u,. It is probably better
however that the linear partial differential equations, which for
any specified function are more convenient than these, should first
be deduced from them *.
From either point of view it is clear that the differential
equations, regarded as given, are sufficient entirely to define the
theta functions.
(4) The case of three variables may be dealt with more
eursorily. Putting
©= Ox, Y= Ox 2= Pn, €= Yn, 1= Pa, $= On,
A= 9221 — PnPx2 + Pa — PsPn,
SF (@) = Mt MEH... + Ages + 427,
iG, DS Soe Pa en al
the fifteen differential equations are
(1) @ss33 — 653 = brs + Age + 4Y, (2) @s352 — 6530s = Aey — ZE + 62,
(3) @sss1 — 6053s = Agz — 2m,
(4) @s32 — 405. — 205300. = $Asy + Nez — 2m,
(5) @s3 — 40320 — 20230n = $252, (6) @ssn — 405 — 2@s30n = 2A,
(7) @s20 — 6 soon = — No — FAL + gy + Agz — OC,
(8) @s1 — 403202 — 2021Qo = — $A + AZ — 2A,
(9) @san — 4s — 2s =o + ZA22,
(10) @si1 — 6Qn@r1 = Aye — Er + vz,
(11) Qs — 6m = —} Ae t+Aghs—SAge + Agsy + AE + Asn — BAGG +12A,
(12) Qa — 6 err = — Zo — EMyAg — B Aw + Ags + As — EASE,
(13) Qn — 4@n — 2QnQn = — brAdg — ZAge— Ary + Ags + bArgn,
(14) @on — 6@n@n = — FAs — 2Zragy + $2 — SAUE+ Ay,
(15) @un — 6@), = ENA — EApAy + ANZ — BAKE + A] + AE.
From the first twelve of them we find the three independent
equations
S=B/P, T=QR/P, U=QYP,
* For the case of p=1, see Weierstrass, Werke, 1. p. 7.
1898.] differential equations defining periodic functions. 52
where P = 2a? + bru? + 2Qay + br,w — 224+ 2E+ EA,,
Q) = 2x°y + bevy + 2xz — E+ YP + Ersy + N+ drs,
R = 2072 + brguz + yz — an + 452 — €,
S = 2x2? + r,2?-— 22y + Er,
T = 2ayz + drgyz + 22— yn — 2E + 4d,
U = 2ay? + drgy + 4yz — 2yE4+ 264+ 4r.
Each of the three relations is, when reduced, of the fourth
degree in the aggregate. We find other relations, also of the
fourth degree, which are deducible from the three above. Of
these two have forms which deserve to be recorded :—
”; E — 2z, y+tnr;, 2a +4r, | =9,
6 —(n+4nr,;), 2€-22+48d,, ytHr,
tM, 26 +420, —(n+ dAs), E— 22
No; ih, g, ui}
z, Y, — 4, i = 0;
& —(7+4rs) 2€-22t+35m, ytsrs
th, 26+ 4r., — (9 + 4s), E — 2z
No, iM, g Y]
if in the first of these determinants we omit #, y, z and replace
E, n, € by «a, y, 2, it becomes identical with the Kummer nodal
quartic obtained in §3; an independent set of three of these
equations is indeed to be regarded as the generalisation of the
Gopel relation to the hyperelliptic case p=3. For any value of
p the generalisation should consist similarly of a set of $p(p—1)
equations in 4p(p+1) Abelian functions. There is a generalisa-
tion in another direction in which there enter 2?—1 Abelian
functions—holding however for the general case of p variables.
(3) On the Total Helipse of the Sun 1898 Jan. 22. By
H. F. Newatt, M.A., Trinity College.
A general account was given of the observations made during
the recent eclipse, and photographs were exhibited, shewing (i) the
general appearance of the corona, (11) the spectrum of the sun’s
limb as photographed with prismatic cameras by Sir Norman
Lockyer’s party, and by Mr Evershed, (11) the spectrum of the
sun’s limb as photographed with a slit-spectroscope by Mr Newall,
and a diagram was shewn illustrating the distribution of glowing
‘coronium’ as observed by Mr Newall with a slitless grating
spectroscope.
Capt. E. H. Hills, R.E., exhibited and described the photo-
522 Mr M°Clelland, On the figures produced [May 16,
graphs obtained by him of the spectrum of the corona, and also
the two series of photographs of the spectrum of the sun’s limb
at the beginning and end of totality.
Monday, May 16, 1898.
Mr F. Darwin, PRESIDENT, IN THE CHAIR.
At a Meeting of the Society held at the Cavendish Laboratory,
B. Cookson, Trinity College, was elected an Associate.
The following Communications were made to the Society :
(1) On the figures produced on photographic plates by electric
discharges. By J. A. MCCLELLAND, M.A., Trinity College.
Several experimenters have lately drawn attention to the
figures produced on photographic plates on development, after
an electric discharge has taken place on to or near the surface
of the plates. The figures are very interesting and well defined,
and differ in a marked degree according as the discharge is
positive or negative.
The manner of the production of these figures seems to be
imperfectly understood, and it has not been shown whether they
are due to a direct chemical action of the discharge on the plate,
or whether they are simply produced by the light of the discharge.
If the figures are produced by a direct chemical action on the
plate it would point to a difference in the manner in which the
positive and negative discharges spread over the plate ; if produced
by the action of light on the plate the figures would be explained
by the different forms of the discharge in the air close to the plate.
In this paper the effect of the gaseous medium surrounding
the discharging point on the form of the figures is investigated,
and also the effect of interposing thin plates of different material
between the film and the discharge. In this way we vary the
form of the visible discharge in the gas close to the plate and
can compare it with the figure produced, and we test the trans-
parency of various substances to the action.
It will appear from the figures given that the effect on the
films is produced principally by the light of the discharge.
The discharge passes through the air quite close to the film
and the sharpness of the lines on the figures is explained by the
nearness of the source of light to the plate, only the part of the
plate just beneath the lines of discharge being affected.
On this explanation the difference in the positive and negative
figures corresponds to the difference in the discharges in air; and
the photographic action brings out these differences very clearly.
1898.] on photographic plates by electric discharges. 523
The figures Nos. 1 to 6 were taken in air at different pressures
as given below.
Positive Negative
No. Pressure. No. Pressure.
1 1 atmosphere 5 1 atmosphere
2. 75 -
Sad i Od »
»”?
The figures were taken with all other conditions the same but
the pressure varied. The photographic plate was laid on a piece
of ebonite and put under a bell-jar in which the air could be
exhausted or compressed; a pointed metal rod just touched the
surface of the film and was connected to the outer coating of a
Leyden jar set on the table, the inner coating of which was
joined to one of the knobs of a Wimshurst machine; the distance
between the knobs was the same in all the figures.
The marked change in the figures produced by a change in
the pressure of the air shows that the form of the figure depends
to a great extent on the form which the discharge takes in the
air near the film; even when the discharging point touches the
film the condition of the air near the film is the principal factor
in determining the nature of the figure.
With the intensity of discharge used the negative figure
shows little detail at atmospheric pressure, while the positive
shows its characteristic fine tapering lines. As the pressure
diminishes both positive and negative figures increase in size
and the negative breaks up into branching feathery lines. At
the lowest pressure given (4 atmos.) the lines in both the positive
and negative figures have broadened out until nearly all the plate
is affected (the negative figure for this pressure is not reproduced
but it was very similar in appearance to the positive).
Figures were also taken for pressures greater than atmospheric,
and as the pressure increases the figures get smaller and smaller,
the positive still showing its fine tapering lines and the negative
becoming a circular spot in which no lines can be detected.
Now when we do the experiments in a dark room and watch
the discharge carefully the form of the visible discharge is the
same, as far as can be judged by the eye, as the form of the
figures; in the positive we see the sharp branching lines and in
the negative we see less distinctness of outline. As the pressure
is lowered the lines broaden out until at the lowest pressures we
see only a continuous flash all over the plate round the dis-
charging point. The photographic figures are the same, but
showing more detail than we can notice with the eye. In the
figures given above the intensity of the discharge is small; it
is interesting to increase the intensity and produce larger figures.
524 Mr McClelland, On the figures produced [May 16,
Figures 7 and 8 are positive and negative taken by placing
the photographic plate on a metal plate connected to the outer
coating of a Leyden jar; the outer coating of a second jar was
joined to a metal rod which just touched the film. The jars were
then charged until a spark passed between their inner coatings.
Here we have the discharge running out in heavy lines, from
each of which at various points branch off small discharges similar
to those in the smaller figures. In the positive the potential rose
high enough to break down the air to the edge of the plate and
on to the metal base, and the greater part of the discharge passed
this way. Even the heavier lines in the negative are less bent
about than in the positive.
To test whether the effects on the film are due to the light
of the spark a number of experiments were made with thin
plates, some transparent to light and some opaque, placed between
the film and the discharging point.
_ With a thin plate of mica on the film the branching lings of
the positive figure are only slightly less distinct than when the
film is uncovered.
Figure 9 is taken with a small circular piece of glass } mm.
thick placed on the centre of the photographic film, and the
discharging point touches the glass. The lines of the positive
figure beneath the glass are quite distinct but broader than they
otherwise would be; we would expect this broadening as the
light is further from the film by the thickness of the glass.
For figure 10 the same piece of glass was used but half of it
was rendered opaque to light by a thin coating of Brunswick
black on the side next the film. Here again the figure comes out
distinct through the transparent part but not through the opaque
part.
In figure 11 part of the film was covered with a piece of
ebonite 4mm. thick; the opaque ebonite entirely shielded the
film although not much thicker than the glass which had little
shielding effect.
These figures seem to prove that the light of the discharge is
necessary to produce the figure on the plate.
As it is well known very perfect impressions of coins or any
metal dies can be obtained by placing them on a photographic
plate and passing a discharge to them. Here again the light of
the discharge from the coin appears to be sufficient to explain
the effect produced. Around the edge of the coin we have a
discharge and also minute discharges from the edges of the raised
portions of it, where the film is affected. Where the coin touches
the film it is not affected.
Figure 12 is taken by weak sparking on a coin laid on a
photographic plate; the edge of the coin is brought out by the
Plate IV.
To face p. 524,
43 * ae
_"
ym tah?
Levee
w
Phil, Soc. Proc. Vol. 1x. To follow Plate IV.
i atom mee Be ine tee meh ati
t
- f Seis De .
Se liad
¥
cu ease nn item Raha Be Lin DERE ta = a tee nese eter remit:
we os \ ty Ab sen a \
0 bE Soot a
1898.] on photographic plates by electric discharges. 525
discharge from it and the letters by the minute discharges from
their edges. Under the parts which touch the film there is no
action, and under the level parts which did not touch there is
weaker action.
We also get a very good impression of the coin if it is laid
on the film and covered with an ebonite plate and the discharge
allowed to pass to the ebonite; with this arrangement we have
an induced discharge around the coin which gives the impression.
If the ebonite is between the coin and the film no effect is
produced.
All these effects on photographic plates would seem to be due,
in great part at least, to the light of the discharge, although the
amount of light may be very small indeed.
That the positive and negative figures differ so radically is
due to the different forms of discharge in air in the two cases ;
the positive is more in the form of a brush and the negative of a
low.
3 Why the nature of the discharge into air from a positive and
a negative point should be so different is a property as yet not
understood.
It is interesting to compare these photographic figures with
the figures produced by sprinkling a mixture of sulphur and
minium on an ebonite plate on which a discharge has passed.
The negatively electrified sulphur adheres to the plate if the
discharge has been positive, the positively electrified minium if
the discharge has been negative.
The positive and negative figures thus produced are very
similar to the photographic figures, only the latter show more
detail. Here again when the pressure of the air surrounding
the plate is reduced the effect is similar to that with the
photographic plate; the radiating lines in the positive become
fainter and broader as the pressure is diminished. This effect
of the pressure of the air has been observed by Joly (Proc. Roy.
Soc. Vol. 47) who concludes that the figures owe their form chiefly
to the manner in which the discharge spreads in the surrounding
air.
In experiments with these dust figures one often gets a
secondary positive in the centre of the primary negative or vice
versa, but this is simply due to a secondary discharge back from
the ebonite to the point used to convey the discharge to the plate.
In fact if we touch with an earthed metal rod a plate of ebonite
which has been electrified by a discharge having passed to it,
we get a figure around the point touched opposite to the sign
of the charge on the plate.
In conclusion I wish to thank Prof. Thomson for the assistance
afforded by his suggestions.
526 Mr Wade, Method of facilitating the measurement [May 16,
(2) On a Method of facilitating the measurement of tem-
perature by means of Platinum Thermometry. By E. B. H.
Wabdk, B.A., Trinity College.
S1. Object of the Paper.
The method of measuring temperatures by finding the
resistance of a platinum wire, claims a high degree of accuracy
and is also widely applicable. Probably one reason why it is not
more frequently used, is that equal increments of resistance do not
represent equal increments of temperature, so that inconvenient
calculations are required to deduce the latter. The object of this
paper is to describe a means of avoiding these calculations. It is
assumed that the formula employed by Callendar and Griffiths is
exact, and if the directions contained in the paper are followed
every unit of resistance will represent the same interval of tem-
perature, which may be 1° Centigrade or any other. It is hoped
that this will lead to the adoption of platinum thermometry by
those who have hitherto been deterred by the calculations.
§ 2. Description of a modification of Wheatstone's Bridge,
which gives direct readings with platinum thermometers.
Fig. 1 represents a form of Wheatstone’s Bridge in which P is
a platinum thermometer having resistance R; at temp. t.
A, B, are coils of equal resistance of a galvanometer. If a
single adjustable resistance were situated between points C, D,
Jip
the whole arrangement would be that in ordinary use. But
in the suggested modification this interval is occupied by two
adjustable resistances in parallel forming a shunt. And these
coils are to be manipulated according to the following rule.
1898.] of temperature by means of Platinum Thermometry. 527
“ By whatever amount the resistance of one arm of the shunt
is increased, that of the other is to be diminished.” Thus the
sum of the resistances of the arms of the shunt is constant.
Let it equal S. It will be shewn that if S is chosen rightly at
the outset, and if the above rule is obeyed, then the condition
that the bridge is balanced is that the arms of the shunt are
linear functions of the temperature. By suitable choice of con-
stants we may make the resistance in one arm numerically equal
to the temperature. ‘The rule is most easily followed by connect-
ing two ordinary resistance boxes in parallel and transferring
plugs from one to the other, so that one box gains in resistance
what the other loses.
§ 3. Demonstration of the accuracy of the Method suggested.
Since the equation connecting resistance and temperature is
that of a parabola with axis inclined, any of the following equa-
tions may be used in which &; is the resistance at ¢, R, the
resistance at 0°, @ is the change of resistance between 0° and
100°.
1 Pi eeet| EES 1 AY 0) /g Rae a ea SEND REG (1),
TPs Gt (TUE a 624 (Oe) ae a (2),
R,— R, ees t ) re
db 100 =6 (1002 a 100} eee rseeeresresense (3).
The constants in the three equations are connected as follows:
C—a2— 07 — ly,
_ (100 + 8) ¢
a= 4 — 28z = ~~ 1002 5
op
SS 2 = 7008"
Now equation (2) can be written as follows :
1
1 i ;
; qeere =
ee) yaa tte)
R=
which will at once be recognized as the expression for the effective
resistance of two conductors in parallel whose individual resistances
are a’ (t+ 2) and a —a’(t+ 2) respectively. Since these two are
each linear functions of the temperature and since their sum is
528 Mr Wade, Method of facilitating the measurement {May 16,
13,
a
B
constant = will in future be called S.
constantly — , the method of § 2 is shewn to be justifiable. The
In order to make this result practically serviceable, it must be
remembered that at the present day it is usual to find the values
of the constants ¢, 5, Ry, (see § 3 equation (3)), in preference to
any three others, and it will be necessary to shew how to obtain
z, a, and S from these quantities.
To find z,
a— a — 27,
Ji, = OG = [BF
ya h, — Cia
RNA
OO OD gob
putting a= GOOe ° B= 1002”
we easily get
22 Coe
OOD Sy ey one
pli te (BE
A
ao
Again a
Po
100:
Ry + 2
ee,
oe
as a control of the accuracy of the calculations we may use
at a’
fy =2— °
Messrs Neville and Heycock have kindly furnished me with
the constants of several pyrometers and from these I have
calculated the values of S, a’, z, which would convert them into
direct reading instruments.
1898.] of temperature by means of Platinum Thermometry. 529
Example 1,
Pyr. 22. d= 99°786, 2= 245771,
o=— (£490) (a2 =— E0858 15:
R, = 257°885, S=7929°71,
[a = 1012728].
ate’
°
a“
Test: 2
257°885,
but Hy = 25:70:885;
Example 2.
Pyr. 25. @= 99-206, 2= 246°765,
S6= 1°5135, a = 1081240,
R= 251000, 8 = 118618,
[a = 1:0070850].
ate = 957-666.
2
but Ry = 257°666.
I have calculated what would be the resistance of these
pyrometers at the melting point of gold (960°), using first
equation (3) of § 3, secondly the rule
Test: z
Rage ere:
S
The exact agreement only proves of course that the arithmetic
and algebra has been correctly performed, but this it seems to me
is all that need be proved. The conclusion is that by using this
form of bridge the same temperature can be arrived at without
calculation as would have been arrived at by the 6 formula.
Whether this method of calculating the temperature is itself
correct is of course outside the object of this paper.
In concluding this note it may be well to point out a curious
analogy between the action of the shunt and the action of the
impurities in the wire. It is regarded by many as not improbable
that in a wire of perfectly pure platinum the resistance might be
a linear function of the temperature, and then no shunt would be
required to give direct readings. If so we may regard the action
of the impurity in the wire as similar to a shunt in providing
an alternative path to the flow of electricity. It seems hardly
worth while to push the idea further in a paper whose object is
entirely practical.
J am greatly indebted to Mr Griffiths and also to Messrs
Neville and Heycock for the assistance received from them.
VOES Ux. PT. VIE 49
530 Dr Willey, The Development of Peripatus, etc. [May 16,
(3) The development of Peripatus novae-britanniae. By Dr
A. WILLEY (Balfour Student).
The ova are without yolk and the nutrition of the embryo
is effected by the development of a large trophic vesicle which
occupies the entire dorsum of the embryo and projects far in
front of the embryo as a head-fold and behind as a tail-fold. The
trophic vesicle is thus a hollow closed cylinder lined internally by
endoderm and externally by ectoderm, the cells of the latter being
adapted for absorption of nutriment. The trophic folds were
compared with the amniotic folds of insects. The trophic cavity
becomes the gastral cavity of the adult and in the transformation
from one to the other the endoderm undergoes certain changes.
It secretes a basal membrane and a cuticular membrane simul-
taneously with a great increase in thickness; and between the
two membranes the endoderm contains numerous small and
large yolk-like globules which are probably to be regarded as
reserve nutrient matter to tide the embryo over the first few
days of its independent life. This late deposition of reserve
nutrient matter derived ultimately from the maternal organism,
as opposed to foreign ingested matter, is probably of some
significance with regard to the question of the lecithality of
the ovum. The embryo lies outside on the ventral surface of the
trophic vesicle just as an insect embryo lies upon the yolk.
(4) On the possibility of deducing magneto-optic phenomena
from a direct modification of an electro-dynamic energy function.
By Mr J. G. Leatuem, M.A., St John’s College.
[Printed in the Transactions, Vol. xv. Pt. I.]
The method initiated by Maxwell for the explanation of the
Faraday effect depended on the direct insertion of a magneto-
optic term in the energy. This method was extended by
Fitzgerald and others to the explanation of Kerr’s effect, namely
the modification introduced im the circumstances of optical
reflexion by magnetisation of the reflector. A difficulty occurred
however in satisfying all the interfacial conditions, which virtually
showed that such a scheme was not formally self-consistent.
The origin of the discrepancy has been traced by Mr Larmor
(Report on the Action of Magnetism on Light, Brit. Assoc. 1893)
to omission to secure what may for shortness be called the
electromotive incompressibility of the medium: in the ordinary
problem of optical reflexion there is no tendency for this to be
disturbed, but when Maxwell’s magneto-optic energy terms are
included the reaction against compression introduces what may be
termed an electric pressure, which must appear in the equations.
1898.] Mr Leathem, On the possibility of deducing, etc. 531
It was necessary to compare the modified scheme thus obtained
with experimental knowledge: and the calculations given in this
paper show that in fact it does not represent the phenomena.
The paper is only a summary of the actual calculations, because
since they were completed the author has shown (On the Magneto-
optic Phenomena of Iron, Nickel and Cobalt, Phil. Trans. 1897)
that the other rigorous theory formulated as an alternative by Mr
Larmor (loc. cit.), which leads to an analytical scheme practically
the same as those advanced on various hypotheses by Fitzgerald,
Goldhammer, Basset, Drude, and others, is in much more satis-
factory agreement with experiment. This brief history of the
subject shows the desirability of the examination of the conse-
quences involved in the former method of explanation: the result
is however what was to be expected by those who adhere to the
more recent formulation (Larmor, A Dynamical Theory of the
Electric and Luminiferous Medium, Part 11., Phil. Trans. 1898)
of optical theory which treats a material medium as free ether
pervaded by discrete molecules involving in their constitution
electrons considered as nuclei of intrinsic zthereal strain. On
such a view a continuous energy function is not the starting
point, and the influence of these discrete nuclei could hardly be
conceived to modify the propagation in the intervening ether in
so fundamental a manner as an electromotive pressure would
demand.
(5) On the solutions of the equation (V? + x?) = 0 in elliptic
coordinates and their physical applications. By R. C. MACLAURIN,
B.A., St John’s College.
[Printed in the Transactions, Vol. xv. Pt. I.]
(6) On the interpretation of divergent solutions of the hyper-
geometric equation. By Mr W. M°F. Orr, Professor at the Royal
College of Science, Dublin.
532 Mr Hargreaves, The Harmonic Expression of the
The Harmonic Expression of the Daily Variation of Solar
Radiation, and the Annual Variation of its coefficients. By
R. Harcreaves, M.A., formerly Fellow of St John’s College,
Cambridge.
[Read 22 November 1897. Revised 1898. ]
A harmonic series, applied to express the intermittent daily
supply of heat from the Sun, consists of a series of terms with the
day, half-day, one-third of a day &c. as periods, and an opening
term on which the total supply for the day depends. Each
coefficient depends on the latitude of the place and on the Sun’s
declination, and through the latter is subject to an annual
variation.
This annual variation for the opening term was discussed
in @ previous communication to the Society*. The present paper
contains the solution for the general case, and tables are appended
giving numerical values for latitudes up to 60°, at intervals
of 10°.
A corresponding analysis of the daily variation of temperature,
and the yearly variation of its coefficients, will be found in a
volume published by the Meteorological Council, under the title
‘Harmonic Analysis of hourly observations of Air Temperature and
Pressure at British Observatories’; and an account of the method
and general results in a paper, bearing the same title, by
Lieutenant-General Strachey, published in the Transactions of
the Royal Society for 1893. I understand that this is practically
the only case in which the Harmonic Analyser has been applied
to the second stage, ze. to express the annual variation of co-
efficients of the daily expansion. The preliminary comparisons -
which I have made of these results of observation, with the
calculations of the present paper, are sufficiently promising to
justify a detailed study, should time permit. But the time and
labour required are very serious, and the reader who gives a
casual glance at the collection of numerical tables appended
here, will hardly realise the weeks of laborious calculation
involved. These tables, with explanations in sections 1 and 5,
are all that is needed for meteorological purposes. Section 3
gives a brief réswmé of properties of the coefficients, which in the
more general form of the mathematical problem, bear a curious
resemblance to the Associated Functions of Laplace.
§1. With a diathermanous atmosphere, the amount of solar
radiation reaching a unit area of the earth’s surface, depends on
* «Distribution of Solar Radiation on the Surface of the Harth, and its depen-
dence on Astronomical Elements,’ printed in Transactions, 1896.
Daily Variation of Solar Radiation, ete. 533
the distance of the sun and the angle of exposure to the sun’s
rays. The element of heat-supply may be written a cos I,
in which dt is time-element, r the distance of the sun from the
earth, and J the sun’s zenith distance. In latitude X, when the
sun’s declination is 6, cos J=sin sin 6 + cosd cos 6 cos; > the
hour-angle varies in the course of the day from —y, to +,
where y, the hour-angle at sunset is given by
sin A sin 6 + cos X cos 6 cos Yr, = 0.
The factor cos J is positive during the day, and at night is replaced
by zero.
In lieu of this discontinuous expression, we propose to write
the quasi-continuous expansion in cosines of multiples of y, in
which y varies from — 7 to + 7, embracing the whole twenty-four
hours. Fourier’s method gives for this
pa Bg COM SUP: te necun tats coats (1),
7?
in which
Vv
Xs =| (sin A sin 6 + cos A cos 6 cos W) cos si dp ...(2).
0
The factor 2 is to be omitted for the opening term (s=0),
on which depends the day’s integral heat-supply, and so the
element of the annual variation discussed in the previous paper.
The other terms express the daily variation divided into harmonic
components, whose periods are the day and its exact sub-
multiples.
Integrating by parts, for the general case
ee cos A cos 6 (= (s—1)y, _ sin(s ae
aS s—l ST
and for the case s=1, ---(3).
cos A. cos 6 :
= ian (hy, — 3 sin 2)
As W, is known in terms of » and 6, these formulae give
numerical values of the coefficients for an assigned latitude and
date of the year. But a general expression for y, may be obtained
in a series of associated Laplace’s functions with sin ) and sin 6 as
arguments, applicable to the whole globe and taking proper account
of the discontinuity that occurs in arctic regions. For greater
generality this is found for
vi
Xop,s =| (sin A sin 6 + cos A cos 6 cos YW)? cos sp dip...(4),
0
534 Mr Hargreaves, The Harmonic Expression of the
the resemblance of which to the mtegral expression for an
associated function, viz.,
[ (2 + Va —1 cost)” cos sy dip,
strikes the eye at once. Physically this corresponds to an
absorbing atmosphere in which the fraction of light or heat
transmitted is (cos/)?—, depending on the angle between the
zenith and the sun’s direction; one factor cosZ being due to the
oblique exposure of a surface.
§ 2. First notice that the conditions for arctic and non-arctic
regions are embraced in the statement that all values yr between
0 and zw, which make sind sind+cosAcos dcosy positive, are
admitted in the integration. During the period of total day Wy,
is continuously 7, and during the period of total night it is 0.
Now if we expand in zonal harmonics a function which = az?
for positive values of 2, and vanishes for negative values, the
coefficient of P,, (#) in the expansion is
1
Ann oie : | aPP,, (@) da
4 Jo
ean p(p—2)...(p—n+2)
2 * (p+) (p+3) Vote aie sagas 0 ())
= 2n+1 v (p=!)(p=3)-..(p=n + 2) oa
2 (p+2)(p+4)...(p+tn+1) ? ”» »
(See Todhunter’s Functions of Laplace, pp. 18 and 19.) Introduce
this expansion in (4), writing sin) sin 6 + cos) cos 6 cos W for w,
and we get
Mea i ; LApyn Pn (sin A sin 6 + cos A cos 6 cos Yr) cos sp dy,
0
the integration being now from 0 to 7, because we have re-
placed the original expression, with its discontinuity and variable
limits, by the quasi-continuous expansion.
With w=sina, w’ = sin 6, we have
P,,(sin \ sin 6 + cos A cos 6 cos yr)
[=s
n—s & =
mee Tey ey Pe) En lee
where P,5(“) = che and the factor 2 1s to be omitted for s = 0.
be
— >
Daily Variation of Solar Radvation, ete. 535
Hence the expansion sought is
\2
ae y)? Pit (0) Py (nu!) » (6).
Xp, SS TrA », n
The formulae quoted for A, ,, though correct, are rather
misleading for the case in which p is an integer ; they suggest
that differences in type turn on x being odd or even, whereas in
reality they depend on p—n being odd or even. Whether n is
odd or even, the group of terms for which p — n is even terminates
with n=p, and the formula is
au WAP se! yt eee (7a).
2 1.3...a~+tp+1).2.4...(p—n)
When p — 1 1s odd and positive, the form is
2n+1 |P
Ron Sa hig aie oes aoe oe
When n=p +1, it is
ila cp bee a 2 aa mie (Tc).
2/) 2210p)
When n — p is odd and greater than 1, it is
2n + 1 - (a — p — 2)
ae ESC EE .(p+n4+]1)
(—1)!-P- (7d).
Thus up to n=p-+1, all terms odd and even occur and all
are positive, beyond this only terms for which n— p is odd occur,
alternately positive and negative, the first negative term being
that for which n=p+3. All the terms for which n ~ p is odd are
embraced in the single formula
an +1 bi 3G a). |p (1p mes
(2° 2.4... (n+p41)(n—p) (n— pt+2)...(n+p)
which will be found to give correctly the three cases (b), (c)
and (d).
The result (6) was obtained for s=0 in the previous paper
by a much more troublesome method.
§ 3. Various sequence formulae may be established directly
from the definition (4). Obviously
Mo a= Xp-1, Si A SIN 6 + 4 cos A cos 8 (Y¥p-1,6-4 + X%p—isi)-+ (8):
536 Mr Hargreaves, The Harmonic Expression of the
Also
+p cos X.cos & (Cgpatnen = i ny) =["> sin W sin sv. cos X cos 8
(sin eo 6 + cos A cos § cos yw)? dyp
= E sin sy (sin X sin § + cos X. cos 8 cos | ‘i +" sx
(sin \ sin 6 + cos A cos § Be eee sidyp,
or SXp,8= FP - COSA CoS 8 (Yip 5 — Xp1, G4) > ceeeae (9).
From (8) and (9) we get
2P Cos cos 6 {(s — 1) Xp—-1,sa — ($+ 1) Xy4, 543}
= (8 — p) Xp,s + PXp—,s8in Asin S...... (10),
which is wanted below.
Again
i (sin cos sap (sin X sin 8 + cos X. cos 6 cos ye}
= (cos cos sv — §. sin sin sip) (sin X sin 6 + cos A cos 8 cos ypyP4
—(p—1)cos2rX cos 8 sin? ap cos syr(sin X sin § + cos X. cos 8 cos pe.
Hence, writing
cosWcossp—s.sinwsinsy=1{(s+ 1)cos(s+1)p—(s— 1)cos(s—1)yp},
and integrating
(p—1)cosr cos sin W cossy (sin X sin 6 + cos X cos 8 cos WP dap
= 4 {(s F 1) Ge = (s = 1) Xp—1,3—i},
or by (10)
a
P(p—1) cos? cos? § | sin’ycossyr(sin \sin 8-+cosd.cos8 cos Wr)? dar
0
= (P — 8") Xp,s — PXp—i,5 SiN D sin 8.
But evidently
vA
cos’ A cos? 6 | cos’ yr cos sy (sin A sin 6 + cos X cos 8 cos yp)? dy
0
= Xp,s — 2X p—1,5 SIN A Sin 6 + Xp—2,3 SIN? A sin? 6.
Hence, multiplying this by p(p—1), and adding to the
previous equation,
P(p—1)Xp-»,5 Cos? X cos? § = (p? — 8°) Xp, — p (2p —1)xp-a,,8in Nsin 8
+ p (p —1) Xp», 5 Sin? A sin? },
Daily Variation of Solar Radiation, ete. 537
or
P(p—1)(cos?rA —sin®d) Xp ~2, s=(p?—S"). Xp,s— p(2p—1) Xp-a,5 Sin Sind
a sequence equation in which only the letter p changes.
The elimination of y,, from (8) and (9) gives an equation in
which only p — 1 occurs, and if we raise by 1 the value of p this is
¥cosr cosd {(s +p +1) Xp, s41 +(S — p—1) Xp, sa} + 5xXp,s8in A sind = 0
the sequence equation in which only the letter s changes.
Further differentiating y,,; with regard to X, we easily obtain
cos X MXee + DX p,s Si A= PY p-1,2 81D 4 .........(18),
and differentiating again
cos X 228 d? a + (p — 1) sin X To. + PXp,s cos A = P sin 8 Signe :
Multiply this by cos), and substitute for psin Xcosd “Aes
and for pcos) sin 3 Sens from (13) (in the latter case with p
reduced to p—1), then
cos* i Ehe.s —sin X cos x Xo + PXp,s COSA
= p’ sin? dX — p (2p — 1) x%p-1,5 Sin Asin 6 + p(p—1)yxpy_-»,,sin? 6.
Simplify the right-hand member by the sequence equation
(11) and divide by cos? X,
Un, : AX rs —
pa nA tt Piet )- a Xv.s=P(P—1)Xp—+,5 (14).
The left-hand member of this equation has the form of
Laplace’s equation for ©, In this case the function is linked
to the alternate one by the right-hand member, which is zero for
the Laplacian.
§ 4. The result (6) for the case in which sin 6 or w= 0, gives the
P
expansion of (1 — »’) in associated functions, an extension of the
es known expansion of (1 — p2)2 in zonal harmonics. With
== ()0
wT
m.|pcos?r
Oe =cosr af cos? yp. cos sda = Sy
"IE (p —s) [s (p +8)
538 Mr Hargreaves, The Harmonic Hupression of the
when p—s is even and = 0,
’ = ()
when p—s is even and < 0,
|p. cos? rX (— jjP@rst-19
~ (s—p) (s— p+2)...(8+p)
when p ~ s is odd.
On the right-hand of (6) the terms of the series which do not
vanish are those for which n — s 1s even, in which case
Jn +s (— Ware
ce 2" |i (w—s) |k(m +8)
Taking p—s even, p—m is also even, and the expansion is
finite, terminating with n=p. ‘Thus s being not greater than p,
n ranges from s to p, and
= Ip Ge we)? BDae Ty (2n +1). |p Bes (ae
24/4 (p —s) E (p +s) 8 21.3...(p+n+1).2.4...(p—n) |n+s
4) z(m—S) n+ s
x See (1 — y?)2 P,* (u)
2” |4 (mn —s) |3(m +8) 4
or
an Bo nap (GIy 2? @p £1). Ju —s |3(p—s) |3 (pts)
(L5H) = Pn: on Biel) 2 Sep =n) hors) S One
(ie LE) oceccmoee| (15)
With p ~ s odd, n ~ p is odd and the series infinite. Thus
p.a- 2)2(— 1} (p+s+ —11°)
(s—p)(s—p+2)...(8 +p)
n=0 7 (2n +1) |p.1.3...(n + p) (— pF tet iy
n=s 2.2.4...(p+n+1)(n—p)(n—pt+2)...(n+p)
es DO? nts
es Gees) ge) ee
mM
» (=p
naw ™(2n+1)1.3...(n+p)(s—p)(s—p+2)...(s+p) |n—s
n=s 229 4. (nt p+1)(n—p)(n—p+2)..(n+p) [E(m=s) |k(n+s)
(AP Gee (16).
=
Daily Variation of Solar Radiation, ete. 539
Remembering that
1 1 \n +8
ee ANS s 2 an ae
[=e ewrde= sq
(15) implies
pts ds P Fo 8) Op Tee
i 32) yt ae fds Sea |jzo Se
\3 ( pe?) 2 dy 8 du = Qn —s)|b(n+s)
AS. (17),
with n, p, s odd or even together, n2s, p2s, p Zn; but if with
n, p, 8 odd or even together, s > p, then the integral vanishes.
In the same way (16) gives for n and s odd or even together
and p the reverse, and either n or p the greater,
[a- pyr “de
a 7.1.3...(0+p)n+s(s—p)(s—pt+2)...(s +p)
GA. (nt prD Mod tw —p\a—p+2)...nep)
For the ® notation the connecting formula is
ln 35 Cl = te) lie (H) =1.3...(2n—1) Or s.
Two particular cases may be noted, viz. those for which s = 0;
(16) then gives for p =—1, 0, and all positive integers *
(p = — 1, opening term 5) :
ee cle ape sic. vise ane
ae (4n+1)1.3...(2n—1)1.3...(2n+2p+ 1)
9.4...In.2.4...(2n4+2p +2)(2n—2p —1)(2n—2p+1)...(2n+2p+1) Pn(u)
vehinens (ES) 3
and similarly (15) gives
(= 1)" (4a +1) Pan (#)
on P— POD, Ste Dp = UNE son $14 Das 2
So ora ga (2u+1)(2n +3)... (Qn + 2p +1) |p pen PNW (20).
, -
* This expansion was obtained directly in Messenger of Mathematics, “Oct. 1896,
p. 92, but the reduction there given is only true for 2n>2p+1. The form above
suits ‘either case. ve
\
ve
540 Mr Hargreaves, The Harmonic Expression of the
§5. Returning now to the particular case of the functions x
required for a diathermanous atmosphere, p= 1, and we need only
1.3...(2n—1)
a
write the s suffix; accordingly with a, =
abbreviation,
7 Ne) ae = We (oar) Or P'm(sind) Pon (sind) )
i= Zcosrcosdt 5 coshcosd > (@n—1)@n+2) ° an (OnE)
|
Xa= - zeosheosdZ Ga Son aD) |
Vs= cos Acos*oS ‘s . |
Pn (Sin) P”'on(sin 8)
(2n—Z)(2n—1) 2n(2n+1)(2n+2)(2n4+8)
Yu= 5 cos hcos'dS - 4
es PP, (sind) PP”, (sin 8)
(2n—3)(2n—2)(2n—1) In (Qn4+1)(Qn+2)(Qn4+3)(2n+4) )
First notice that all these coefficients vanish at the poles, as
they should do, for there is no daily variation proper at the poles.
Again, sind, sind change signs, one in passing from northern
to southern hemisphere, the other in passing through the equinoxes ;
cos A, cos 6 do not change sign.
7
4,
remaining odd terms, y;v;... are entirely odd, y.y,... entirely even,
conclusions which may be drawn directly from (3). When sin 6 is
expressed in terms of solar longitude by the relation
sin 6 =sinesin 0,
Hence we see that x, has a single even term = cos X cos 6, the
X3X5--- and the odd part of x, have the form
a, sin 0+ a;sin 30 +a;sin 50 +...,
X2X, and the even part of yx, have the form
My + a cos 20 + a,cos 40 +....
Where ar.odd power of cos 6 occurs, an elliptic integral is wanted
to complete the harmonic expression, thus the even part of y,, viz.
T cos dcos = cos 0 (5 + E, cos 20+ EF, cos 40...)
= cos X. (‘7533 + ‘0324 cos 20 — 0003 cos 4@...),
Daily Variation of Solar Radiation, ete.
E.,, being used for the integral
Tv
[0s 5. cos 2n6dé,
0
2
or | /1 —sin?e sin? @. cos 2nOdé.
0
The series (21) converge only slowly; they have been used to
confirm other work for the latitude of Greenwich and for latitude
60°, but in the absence of tables of associated functions calculated
with reference to angle, the labour entailed is absolutely pro-
hibitive. Accordingly in the case of the even functions yx, 4...
the formula (3) was used to give particular values for 6 = 0°, 30°,
60°, 90°. Knowing the form of the expansion, these are sufficient
to determine a) a,a,a,; on the assumption that as and subsequent
coefficients are negligible. The tabulated results for y, obtained
in the previous paper (Q there) were obtained directly from finite
formulae involving elliptic integrals, and shewed a rapid con-
vergence in the numbers a, a,..., although in that case also the
convergence of the zonal harmonics was slow. The expectation
that this would also prove to be the case for y,... was confirmed
by the small values obtained for ag, so small that although a, was
always included in the work, its values are not tabulated, as they
only just come into the 4th place of decimals for latitudes 50° and
60°. For the odd functions y;y;... and the odd part of y, only
the values for 30°, 60°, 90° are available ; sufficient to give a, a, a;
on the assumption that subsequent terms may be neglected. Here
also the values of a; turned out very small. The calculations were
made to 6 places, and two are suppressed.
As regards the tables it should be mentioned that when
_ a0
a
dt
is used, formula (1) becomes
2Hdé
FO hyn + En c08 9H
in which the y’s depend on @ as shewn in table (A). With one
year for the unit of time h=2zab, also d@ =27dt [1 + small
quantities depending on eccentricity].
The transformation to mean time is made as in § 17 of the
previous paper, the product x,d@ becoming 27yx,'dt, so that
formula (1) then stands
2H
a dt [4x + Xx cos sr],
542 Mr Hargreaves, The Harmonic Expression of the
and accordingly the y, functions tabulated in (B) contain the
correction for the varying distance of the sun. For abbreviation
¢ is written for 27t. The even terms give no difference between
northern and southern hemispheres, for y; the sign is to be
changed throughout for the southern hemisphere, for x with
both odd and even terms, the effects are more complicated and
results given for both hemispheres,
(A) Table of y’s expressed as harmonic functions of sun’s
longitude measured from the vernal equinox.
Xi = a) + a, sin 6 + a, cos 20 + a, sin 30 + a, cos 40 + ...
A= O 7533 ‘0 0324 0 — 0003
10° ‘7419 ‘0691 0319 “0 —-0003
20° ‘7079 1357 ‘0305 ‘0002 — 0003
30° 6524 ‘1976 0280 ‘0008 — ‘0003
40° sonal 2516 ‘0248 ‘0015 — 0002
50° “4842 2946 0208 ‘0038 — ‘0002
60° ‘3767 3190 ‘0162 0095 — 0002
Yo = Ay + dy cos 20 + a, cos 40. Vs = a, sin @ + a; sin 36.
A= O° 3197 +:01388 —-0001 N= 10> 50229) 20
10° 3140 0144 — -0006 20° —-0441 —-0004
20° +2952, (0183 —-0002 30° —:0618 —-0016
30° :2648 0242 — -0003 40° — 07338 —:0042
AOS © ON ‘0330 — 0004 50° — 0737 —-0097
50° -1689 0455 —-0002 60° —-0531 —-0204
60° 1037 ‘0616 +0017
Xs = Ay + a, cos 20 + a, cos 40.
w= OF — 0639 — ‘0028 =P
10° — 0618 — 0039 + 0001
20° — 0550 — 0078 — 0001
30° — 0439 — ‘0139 + 0000
4()° — ‘0289 — 0217 — ‘0001
a0 — 0115 — -0290 — 0025
60° + 0025 — 0272 — 0087
545
Daily Variation of Solar Radiation, ete.
(Fr + PF) 809 2 TOO. + (2% + PE) S00 ZEOO-— CL .@6 + PZ) 8099190.—( _.¢ +P) 809 GEOO. + LEOT.
(FF + Ph) $09 ZOO0. — (ZZ + PE) $09 ZOO. — (Z_ BS + PZ) 809 CCFO. — CFE .Z + P) 809 F900. + GSOT-
(FF + PF) 809 F000. — (.6Z + PE) 800 S100. -—CF ZZ + PZ) $00 6EEO. — C1E .1 + P) 809 OSOO. + LZZS-
(PF + PF) $00 E000. — (.2Z + PE) 800 Z100.— CL .6G + PZ) 800 SFZO- — CLF .0 + P) 809 1600. + SF9Z
(FF + PF) 809 ZOO: — (cE + PE) 809 6000. — COT .2% + PZ) $09 ZSTO. — (OF .0 + P) $09 ZOTO- + SS6E.
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INDEX TO VOLUME IX.
Abelian functions (BAKER), 381.
Alloy, Superficial colour of a silver zinc (HEycock and NEvILLE), 222.
Roéntgen photographs of metallic (Heycock and NEvILue), 417.
Amphioxus, Formation of germinal layers in (MacBripe), 150.
and Balanoglossus, The relationship of (MacBripr), 309.
ANDERSON, A., On the maximum deviation of a ray of light by a prism, 195.
On the apparent electrification at the bounding surface of two dielectrics,
292.
Annual General Meeting, 1895, 1.
Bee ea. 1806. 201.
1897, 323.
Assimilation in aquatic plants, Effects of water currents on (DARWIN and
Pertz), 76.
—— Farmer’s method of demonstrating (DARWIN), 338.
Associates elected, 215, 258, 373, 522.
Astronomical elements, Solar Radiation and its dependence on (HARGREAVES),
61.
Atomic weight of oxygen (Scorr), 143.
Baker, H. F., On the Gamma Function, 332.
— On the lines of striction of a hyperboloid, 333.
— Abelian functions in connexion with two-dimensional fluid motions, 381.
—— On a certain system of differential equations defining periodic functions,
513.
Balanoglossus and Amphioxus, Relationship between (MacBripe), 309.
Batt, Sir R. §., On a point in theoretical dynamics, 193.
Bariow, Dr Lazarus, On an osmometer, 72.
BatEmMay, Rev. P. E., Elected Fellow, 1897, Apr. 26, 292.
Bateson, W., Discussion of Dr Gaskell’s paper, 39.
—- Notes on hybrid Cinerarias produced by Mr Lynch and Miss Pertz, 308.
Bennettites, On the leaves of (SEWARD), 273.
VOL. IX. PT, VIU, 43
546 Inder.
Brack, A., Reduction of a certain Multiple Integral, 332.
BuackMAN, F. F., Phenomena of Carbon Dioxide production associated with
reduced vitality in plants, 273.
Bigs, E. J., Discussion of Dr Gaskell’s paper, 42.
—— Communication between peritoneal cavity and renal veins through
nephrostomial tubules, 73.
BuiytHE, W. H., Forms of cubic surfaces containing 27 real straight lines, 6.
BorRADAILE, L. A., Elected Fellow, 1895, Nov. 25, 17.
Brappsory, Prof. J. B., Elected Fellow, 1896, Apr. 27, 141.
Brain with the chrome-silver method, Results obtained by staining the
(HILL), 235.
Britt, J., Generalization of certain properties of the tetrahedron, 98.
BurKILL, I. H., Collection of plants from New Britain (Neu Pommern), 90.
Cathode Rays (THomson), 243.
Cavs, CHARLES, Elected Fellow, 1896, Feb. 24, 97.
CureEB, Dr C., Equilibrium of isotropic elastic solid ta 61.
—— Tides on the equilibrium theory, 318.
Cinerarias, Notes on hybrid (BATEson), 308.
Coatss, W. M., Elected Fellow, 1897, Apr. 26, 292.
Compression of certain rarefied gases, On luminosity attending the (NEWALL),
295.
Connecting threads in the cell wall, Method for demonstration of (GARDINER),
504.
Coral reefs (GARDINER), 417.
Crania found at Girton in 1881 (Horton-SmitnH), 111.
—— From Teneriffe (SHRUBSALL), 154.
Cubic surfaces containing 27 straight lines, Forms of (BLYTHE), 6
Darton, J. H. C., Elected Fellow, 1898, Feb. 7, 398.
Darwin, F., and Miss D. F. M. Prertz, Effect of water currents on the
assimilation of aquatic plants, 76.
— On the injection of the intercellular spaces occurring in the leaves of
Elodea during recovery from plasmolysis, 272.
—— Observations on stomata by a new method, 303.
—— Farmer’s method of demonstrating assimilation, 338.
Dewar, Prof. J., Experiments on liquid air, 97.
Differential equation of the first order, On Lie’s solution of a (Dixon), 279.
Differential equations defining periodic functions, On a certain system of
(BAKER), 513.
Diffraction pattern near the focus of a telescope (MAYALL), 259.
Dioxymaleic acid and its derivatives (FENTON), 142.
Drxon, A. C., On a method of discussing the plane sections of surfaces, 198.
— On Lie’s solution of a partial differential equation of the first order, 279,
Dixon, E. T., On the theory of order, 513,
Index. 547
Duckwortu, W. H., Elected Fellow, 1896, Feb. 10, 72.
Dynamics, On a point in theoretical (BALL), 193.
EASTERFIELD, and T. B. Woop, The constituents of Indian hemp, 144.
Echinid larvae, On the continuity of Mesenchyme cells in (MAcBripg), 153.
Eclipse of the Sun, 1898 Jan. 22, Total (NEWALL), 521.
Elastic solid shells, Equilibrium of (CHREE, C.), 61.
Electric discharge, Expansion produced by (Marttn), 11.
In vacuo (MoncKMAN), 216.
—— On the figures produced on photographic plates by (M°CLELLAND), 522.
—— Waves and Réntgen Rays, Longitudinal (THomson), 49.
Electrical oscillations in wires (PocKLINGTON), 324.
Properties of newly prepared gases (TOWNSEND), 345.
Electrification at the bounding surface of two dielectrics, On the apparent
(ANDERSON), 292.
Eliminant of two algebraic equations, On the degree of (LACHLAN), 313.
Encephalartos Ghellinckii (Sewarp), 340.
Expansion produced by electric discharge (MARTIN), 11.
Farmer’s method of demonstrating assimilation (DARWIN), 338.
Fenton, H. J. H., On dioxymaleic acid and its derivatives, 142.
FuetcHer, W. M., Elected Fellow, 1898, Feb. 7, 398.
Flints from Plateau gravel at Salisbury, Chipped (HuauHss), 120.
ForsytH, Prof. A. R., Partial differential equations of the second order, 345.
On some differential equations in the theory of symmetric algebra, 401.
Frog, Communication between peritoneal cavity and renal veins through
nephrostomial tubules in the (BuEs), 73.
Gapow, H., Discussion of Dr Gaskell’s paper, 39.
— On the supposed relationship of Birds and Dinosaurs, 204.
Gau.op, E. G., Change of the independent variable in a coefficient, 272.
Gamma Function (BAKER), 332.
GARDINER, J. STanLEy, Elected Fellow, 1898, May 2, 513.
— Coral Reefs of Funafuti, Rotuma and Fiji, 417.
GARDINER, WALTER, Method for demonstration of connecting threads in the
cell wall, 504.
Gases, Electricity in gases and the formation of clouds in charged (TownsEND),
244,
— Electrical properties of (TowNsEND), 345.
GasKELL, Dr W. H., The origin of Vertebrates, 19.
Geological history of monocotyledons (SEWARD), 110.
Grack, J. H., On circles, spheres and linear complexes, 332.
GriFFitHs, E. H., On thermometric “Fixed points,” 224.
Happovy, A. C., Elected Fellow, 1897, Feb. 8, 243.
HarcGrEAVES, R., Elected Fellow, 1896, Mar. 9, 110.
548 Index.
Hareruaves, R., Distribution of solar radiation and its dependence on
Astronomical Elements, 69.
Harmer, Dr S. F., Discussion of Dr Gaskell’s paper, 38.
—— On cyclostomatous Polyzoa, 208.
On the casts of Iguanodon bernissartensis, Boulenger, 202.
Hawaiian Insects (PERKINS), 373.
Henry, J., Effect of ultra-violet light on the conductivity of iodine vapour, 319.
Heycock and NEVILLE, Superficial colour of a silver zinc alloy, 222.
— R®éntgen photographs of metallic alloys, 417.
Hit, Dr A., Some results obtained by staining the Brain with the chrome-
silver method, 235.
Hits, Capt. E. H., On the Total Eclipse of the Sun, 1898 Jan. 22, 521.
Honorary Members, Elected 1897, May 24, 309.
Horton-Smita, R. J., Description of crania found at Girton in 1881, 111.
Hovuau, S. S., Elected Fellow, 1898, Apr. 26, 292.
Huaues, Prof. T. M°K., Exhibition of specimen of Travertine lining wooden
pipe, 17.
—— Symmetry in the foliage of Mulberry with asymmetry in individual
leaves, 18.
— On the Recurrence of Ice Ages, 114.
— Chipped Flints from the Plateau gravel of Salisbury and elsewhere, 120.
Horst, G. H. J., Elected Fellow, 1896, Nov. 23, 222.
Hysteresis, Method of measuring loss of energy in (SEARLE), 2.
Ice Ages, Recurrence of (HuGHEs), 114.
Iguanodon bernissartensis, Boulenger, On the casts of (HARMER), 202.
(GapDow), 204.
Indian hemp resin, On the constituents of (HASTERFIELD and Woop), 144.
—— Pharmacological action (MARSHALL), 149.
Iodine vapour, Effect of ultra-violet light on the conductivity of (Hmnry), 319.
Kathode Rays (THomson), 243.
—— (THomMsON and SKINNER), 371.
KERR, J. GRAHAM, 380.
Lacu3an, R., Elected Fellow, 1897, Apr. 26, 292.
—— On the degree of the eliminant of two algebraic equations, 313.
Larmor, J., On the absolute Minimum of optical deviation through a prism,
108.
—— On the period of the Earth’s free Eulerian precession, 183.
On the theory of osmotic pressure, 240.
Leakage of electricity through dielectrics traversed by Réntgen rays (THom-
Son and M°CLELLAND), 126.
Index. 549
LeatHem, J. G., On the deduction of magneto-optic phenomena from an
electrodynamic energy function, 530.
Lie’s solution of a partial differential equation of the first order (D1xon), 279.
Lister, J. J., Quinqueloculine arrangement of the chambers in the young of
Triloculina and Biloculina, 236.
LivEine, Prof. G. D., On photographing the whole length of a spectrum at
once, i141.
LiversipG£, A., Elected Fellow, 1897, Feb. 22, 258.
Longitudinal Electric Waves and Réntgen Rays (THomson, J. J.), 49.
MacBripg, E. W., Discussion of Dr Gaskell’s paper, 37.
—— Note on the formation of the germinal layers in Amphioxus, 150.
—— On the continuity of Mesenchyme cells in Echinid larve, 153.
The relationship between Amphioxus and Balanoglossus, 309.
M°CLELLAND, J. A., and THomson, Leakage of electricity through dielectrics
traversed by Réntgen rays, 126.
M°CLELLAND, J. A., On the figures produced on photographic plates by
electric discharges, 522.
Macponatp, H. M., Elected Fellow, 1896, Nov. 23, 222.
MAc.LaAuRIN, R. C., On the solutions of the equation (y?+.«?) ~=0 in elliptic
coordinates, 531.
MacManovy, Major P. A., A new method in Combinatory Analysis, 381.
Magneto-optic phenomena, On the deduction of (LEATHEM), 530.
MarsHat.t, C. R., Note on the pharmacological action of cannabis resin, 149.
MarsHALL Warp, Prof. H., Elected Fellow, 1896, Feb. 10, 72.
—— Artificial cultures of Stereum, a timber-destroying fungus, 340.
Martin, Miss, Expansion produced by electric discharge, 11.
Maximum deviation of a ray of light through a prism (ANDERSON), 195.
Mayatt, R. D. H., On the diffraction pattern near the focus of a telescope, 259.
Melanesia (WILLEY), 398.
Mesenchyme cells in Echinid larve (MacBrips), 153.
Minimum of deviation through a prism, Absolute (LARMOR), 108.
Monckman, Dr J., On certain cases of discharge in vacuo and on the zigzag
path of lightning, 216.
Monocotyledons, Geological history of (SEwarRD), 110.
Mulberry, symmetry in foliage of a branch of (HucHEs), 18.
Nephrostomial tubules in frog, Communication between peritoneal cavity and
renal veins (BLES), 73.
NrviILLE and Hrycock, The superficial colour of silver zinc alloy, 222.
New Britain (Neu Pommern), Collection of plants from (BURKILL), 90.
Newatt, H. F., Spectroscope used in connexion with the 25-inch refractor,
179.
—— A suggestion for a form of spectroheliograph, 179.
550 Index.
Newatt, H. F., On the marks made by stars on photographic plates near the
focus of a telescope, 269.
— On luminosity attending the compression of certain rarefied gases, 295.
— On the Total Eclipse of the Sun, 1898 Jan. 22, 521.
Origin of Vertebrates (GASKELL), 19.
Orr, W. M°F., Theorems on the contacts of spheres, 271.
— On the interpretation of divergent solutions of the hypergeometric
equation, 531.
Osmometer (Dr Lazarus BAaRLow), 72.
Osmotic pressure, On the theory of (LAaRMOR), 240.
PARKIN, J., Elected Fellow, 1896, Feb. 24, 97.
Peripatus nove britanniz, On the development of (WILLEY), 530.
PERKINS, R. C. L., Notes on some Hawaiian Insects, 373.
Pertz, Miss D. F. M., and Mr F. Darwty, Injection of intercellular spaces
in leaves of Elodea during recovery from plasmolysis, 272.
—— Effects of water currents on assimilation of aquatic plants, 76.
Phosphorescence in gases (NEWALL), 295.
Photographic plate, Effect of zinc and other metals on a (THOMSON), 372.
Figures produced by electric discharges on (M°CLELLAND), 522.
Platinum Thermometry, On a method of facilitating (WADE), 526.
Pocxiineton, H. C., Electrical oscillations in wires, 324.
Polyzoa, Cyclostomatous (HARMER), 208.
Precession, On the period of the earth’s Free Eulerian (LARMor), 183.
Prism, Absolute minimum of deviation through a (LARMoR), 108.
Maximum deviation of a ray of light through a (ANDERSON), 195.
Quinqueloculine arrangement (LISTER), 236.
Ramsry, A. 8., Elected Fellow, 1898, Feb. 7, 398.
REYNOLDS GREEN, Dr J., Elected Fellow, 1896, Feb. 24, 97.
Rosson, H. C., Elected Fellow, 1897, Feb. 22, 258. f
Réntgen Rays, Longitudinal Electric Waves and (THomson, J. J.), 49.
— Leakage through dielectrics traversed by (THomson, J. J., and
M°CLELLAND, J. A.), 126.
— On the nature of (SToKEs), 215.
— On the diffuse reflection of (THomsoN), 393.
— Photographs of metallic alloys (Hrycock and NEVILLE), 417.
RUTHERFORD, E., The discharge of electrification by ultra-violet light, 401.
Scort, A., On the atomic weight of oxygen, 143.
—— On the combining volumes of carbon monoxide and oxygen, 144.
Index. 551
SEARLE, G. F. C., Method of measuring the loss of energy in Hysteresis, 2.
Sections of surfaces, Method of discussing plane (Dixon), 198.
SEDGWICK, A., Discussion of Dr Gaskell’s paper, 37.
SEDGewWICK, W. F., Elected Fellow, 1898, May 2, 513.
SEwarp, A. C., Notes on Geological History of Monocotyledons, 110.
— On the leaves of Bennettites, 273.
— On Encephalartos Ghellinckii, Lem., a rare Cycad, 340.
Surerey, A. E., Discussion of Dr Gaskell’s paper, 40.
SHRUBSALL, F. C., Crania from Teneriffe, 154.
SKINNER, S., and THomson, Chemical effect of kathode rays, 371.
Solar Radiation, Distribution of, and its dependence on Astronomical
Elements (HARGREAVES), 61.
Spectroheliograph, A suggestion for a form of (NEWALL), 179.
Spectroscope used in connexion with 25-inch refractor (NEWALL), 179.
Spectrum at once, On photographing the whole length of a (LivEtrNe@), 141.
Spheres, Theorems on the contacts of (ORR), 271.
Stoxss, Sir G. G., On the nature of the Réntgen Rays, 215.
Stomata by a new method, Observations on (DARWIN), 303.
Surfaces, Method of discussing the plane sections of (Drxon), 198.
Symmetry in foliage of mulberry (HuGHEs), 18.
Teneriffe, Crania from (SHRUBSALL), 154.
Tetrahedron, Generalization of certain properties of the (BRILL), 98.
Thermometric fixed points (GRIFFITHS), 224,
Tuomson, Prof. J. J., Longitudinal Electric Waves and Réntgen Rays, 49.
—— On the cathode rays, 243.
—— HEffect of zinc and other metals on a photographic plate, 372.
-—— On the diffuse reflection of Réntgen Rays, 393.
— and J. A. M®Crienianp, Leakage of Electricity through Dielectrics
traversed by Réntgen Rays, 126.
— and S. Skinner, A chemical eftect produced by the impact of kathode
rays, 371.
TownsEnD, J. S., On electricity in gases and the formation of clouds in
charged gases, 244.
Electrical properties of newly prepared gases, 345.
Travertine lining a pipe, Specimen of (HUGHES), 17.
Triloculina and Biloculina, Quinqueloculine arrangement of chambers in the
young of (LISTER), 236.
Ultra-violet light on the conductivity of iodine vapour, Effect of (HENrRy),
319.
— On moist air, Production of a cloud by action of (WILsoN), 392.
The discharge of electrification by (RUTHERFORD), 401.
Uranium rays on the condensation of water vapour, Action of (WILSON), 333,
552 Index.
Vertebrates, The origin of (GASKELL), 19.
Vincent, J. H., On the use of logarithmic coordinates in physics, 393.
Wane, E. B. H., A method of facilitating the measurement of temperature
by means of Platinum Thermometry, 526.
Watts, A. J., Elected Fellow, 1896, April 27, 141.
Wittey, A., Some zoological results of a voyage to Melanesia 1894—1897,
398.
— The development of Peripatus novee britanniz, 530.
Witson, C. T. R., Elected Fellow, 1896, April 27, 141.
— On the action of Uranium rays on the condensation of water vapour,
333.
— On the production of a cloud by the action of ultra-violet light on
moist air, 392.
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| |
Cambridae :
PRINTED AT THE UNIVERSITY PRESS,
AND SOLD BY
DEIGHTON, BELL & CO. AND MACMILLAN & BOWES, CAMBRIDGE.
G. BELL AND SONS, LONDON, |
1898
Price Two Shillings and Sixpence.
31 October, 1898.
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